I was not sure I would have to do much of a fishless cycle on my new 5 gallon / 19 litre Quarantine/Hospital tank. That is apparently what is happening, though, in spite of transferring 100% mature media from my main 26 gallon tank. So I'll go ahead and log my setup and results in case it ever helps anyone else.
EDIT: I went almost two weeks using the tiny built-into-the-hood filter pictured here:
But then I gave up and installed an Aquaclear 20 HOB (rated up to 20 gallons). So my original post has been altered. Pictures included after the log...
TAP WATER STATS: (tested directly from the faucet)
Ammonia = 0.25 ppm
Nitrite = 0.00
Nitrate = 0.00
pH..... = 7.2 (this goes down to 6.4 after water sits for a day or two)[/font]
AQUARIUM WATER STATS: (water was dechlorinated)
A = Ammonia
NO2 = Nitrite
NO3 = Nitrate
Adding 0.60 ml of ammonia as needed.
Day..Date.....Time.....A.......NO2.....NO3.....pH.....Temp(F)....NOTES
1....Oct09....23:00....4.00....0.00....0.00....8.2...............Added 0.60 ML of ammonia & 1 1/2 tsp baking soda
2....Oct10....14:15....4.00....................8.4....
3....Oct11....08:30....4.00....................8.2....83.7F......
4....Oct12....08:45....4.00...........................83.7F......
5....Oct13....10:15....4.00...........................84.2F......
6....Oct14....14:45....4.00...........................84.2F......
8....Oct16....14:10....2.00....0.00............8.4....84.4F......
10...Oct18....08:30....1-2.....0.00............8.2....83.2F......
Day..Date.....Time.....A.......NO2.....NO3.....pH.....Temp(F)....NOTES
11...Oct19....13:15....1+ .....0.00............8.2....84.1F......
12...Oct20....13:55....1.00....0.00............8.2....84.9F......
13...Oct21....08:20....1.00....0.00............8.4....84.8F......
14...Oct22....12:40....1.00....0.00....5.00....8.4....84.5F......
15...Oct23....20:55....1.00....0.00..............................+0.60 ml ammonia after tests were done
16...Oct24....19:20....4.00....0.00...................84.8F......
17...Oct25....09:00....4.00....0.00....5.00....8.2....84.1F......
18...Oct26....19:50....4.00....0.00............8.2....84.7F......
19...Oct27....08:50....2-4.....0.00....10.00..........84.6F......
20...Oct28....07:45....1-2.....0.00............8.2....84.9F......
Day..Date.....Time.....A.......NO2.....NO3.....pH.....Temp(F)....NOTES
21...No tests
22...Oct30....12:30....1.00....0.25....10-20...8.4....83.2F......
23...Oct31....Witches...Pumpkins...Goblins...Vampires............
At this point, ammonia added each morning to raise it to 4 ppm due to evening readings of zero ammonia.
Day..Date.....Time.....A.......NO2.....NO3.....pH.....Temp(F)....NOTES
24...Nov01....08:45....0.00....0.25............8.4....82.9F......
25...No tests
26...Nov03....08:00....0.00....5.00....40.00...8.2....83.4F......
27...Nov04....09:30....0.00....5.00....10.00...8.2....83.2F......50% water change
28...Nov05....09:30....0.00....5.00....10.00...7.8....83.7F......+1/4 tsp baking soda
29...Nov06....09:15....0.00....1.00............8.4....83.1F......
30...Nov07....08:55....0.00....5.00....10.00...7.4....83.6F......+1/2 tsp baking soda
31...Nov08....07:51....0.00....1.00............8.2....82.0F......90% water change; +1 tsp baking soda
32...Nov09....21:20....0.00....1.00............8.2...............
33...Nov10....08:21............0.00....40.00...8.4....83.2F......
SETUP:
1. 5 Gallon (19 Litre) bow front acrylic tank
2. Tank dimensions: 14 in wide x 10.5 in tall x 10 in deep (depth from center of bow front)
3. Aquaclear 20 hang-on-back power filter (100 gallons per hour)
4. Tank temperature set to 83 F (give or take)
6. API Master test kit
7. No live plants
8. 25 watt heater
(tank decorated by my kids - all you natural purists leave me alone!
)
In order to install the Aquaclear on the back of the tank, I had to cut a notch out of the part of the lid that supported the old filter:
This gave me enough room to hang the filter on the back, and still have the light hood fit okay:
NOTE: the first few replies from Waterdrop below are from when my original post was written for the built-in filter. I had some questions about it. Sorry if it's confusing.
EDIT: I went almost two weeks using the tiny built-into-the-hood filter pictured here:

But then I gave up and installed an Aquaclear 20 HOB (rated up to 20 gallons). So my original post has been altered. Pictures included after the log...
TAP WATER STATS: (tested directly from the faucet)
Ammonia = 0.25 ppm
Nitrite = 0.00
Nitrate = 0.00
pH..... = 7.2 (this goes down to 6.4 after water sits for a day or two)[/font]
AQUARIUM WATER STATS: (water was dechlorinated)
A = Ammonia
NO2 = Nitrite
NO3 = Nitrate
Adding 0.60 ml of ammonia as needed.
Day..Date.....Time.....A.......NO2.....NO3.....pH.....Temp(F)....NOTES
1....Oct09....23:00....4.00....0.00....0.00....8.2...............Added 0.60 ML of ammonia & 1 1/2 tsp baking soda
2....Oct10....14:15....4.00....................8.4....
3....Oct11....08:30....4.00....................8.2....83.7F......
4....Oct12....08:45....4.00...........................83.7F......
5....Oct13....10:15....4.00...........................84.2F......
6....Oct14....14:45....4.00...........................84.2F......
8....Oct16....14:10....2.00....0.00............8.4....84.4F......
10...Oct18....08:30....1-2.....0.00............8.2....83.2F......
Day..Date.....Time.....A.......NO2.....NO3.....pH.....Temp(F)....NOTES
11...Oct19....13:15....1+ .....0.00............8.2....84.1F......
12...Oct20....13:55....1.00....0.00............8.2....84.9F......
13...Oct21....08:20....1.00....0.00............8.4....84.8F......
14...Oct22....12:40....1.00....0.00....5.00....8.4....84.5F......
15...Oct23....20:55....1.00....0.00..............................+0.60 ml ammonia after tests were done
16...Oct24....19:20....4.00....0.00...................84.8F......
17...Oct25....09:00....4.00....0.00....5.00....8.2....84.1F......
18...Oct26....19:50....4.00....0.00............8.2....84.7F......
19...Oct27....08:50....2-4.....0.00....10.00..........84.6F......
20...Oct28....07:45....1-2.....0.00............8.2....84.9F......
Day..Date.....Time.....A.......NO2.....NO3.....pH.....Temp(F)....NOTES
21...No tests
22...Oct30....12:30....1.00....0.25....10-20...8.4....83.2F......
23...Oct31....Witches...Pumpkins...Goblins...Vampires............
At this point, ammonia added each morning to raise it to 4 ppm due to evening readings of zero ammonia.
Day..Date.....Time.....A.......NO2.....NO3.....pH.....Temp(F)....NOTES
24...Nov01....08:45....0.00....0.25............8.4....82.9F......
25...No tests
26...Nov03....08:00....0.00....5.00....40.00...8.2....83.4F......
27...Nov04....09:30....0.00....5.00....10.00...8.2....83.2F......50% water change
28...Nov05....09:30....0.00....5.00....10.00...7.8....83.7F......+1/4 tsp baking soda
29...Nov06....09:15....0.00....1.00............8.4....83.1F......
30...Nov07....08:55....0.00....5.00....10.00...7.4....83.6F......+1/2 tsp baking soda
31...Nov08....07:51....0.00....1.00............8.2....82.0F......90% water change; +1 tsp baking soda
32...Nov09....21:20....0.00....1.00............8.2...............
33...Nov10....08:21............0.00....40.00...8.4....83.2F......
SETUP:
1. 5 Gallon (19 Litre) bow front acrylic tank
2. Tank dimensions: 14 in wide x 10.5 in tall x 10 in deep (depth from center of bow front)
3. Aquaclear 20 hang-on-back power filter (100 gallons per hour)
4. Tank temperature set to 83 F (give or take)
6. API Master test kit
7. No live plants
8. 25 watt heater

(tank decorated by my kids - all you natural purists leave me alone!
In order to install the Aquaclear on the back of the tank, I had to cut a notch out of the part of the lid that supported the old filter:

This gave me enough room to hang the filter on the back, and still have the light hood fit okay:


NOTE: the first few replies from Waterdrop below are from when my original post was written for the built-in filter. I had some questions about it. Sorry if it's confusing.