Yes... in a small holding container, the fish will be fine for how long the water change will take. Having waited this long though, I wouldn't recommend a 100% change today. I'd recommend a 50% change today and a 100% change in 2 days after that, followed by the continual changes moving forward.
Do you have a filter on this tank? A small sponge filter (powered by an air pump) would be sufficient. And these can be easily cleaned during routine water changes with a quick squeeze in the old tank water to remove any detritus (waste) that accumulates.
The water change itself is simple... remove the water through water means you wish - a tank that small could just be dumped out - or by siphoning the water. Then refill the tank with DECHLORINATED (you can buy a bottle of dechlorinator cheaply that will last a good while, you'll only need a drop or two for that size tank), TEMP MATCHED tap water. The key to success in a case like this is the water needs to be the same temperature (or within a degree or so) of the water the fish has been in. Failing that can cause temperature shock to the fish, which can weaken them making them susceptible to disease.
Floating the holding container in the tank for about 15 minutes after the water change can help to deal with any temperature differences and make the transition back to the tank less stressful. Also, if you can catch the betta in the holding container and avoid netting him, that would also be less stressful for him.
(Be sure to place a kitchen towel or something over the top of the container, as bettas are known to be jumpers... and you don't want to find Henry on the floor during the water change. Hopefully the tank you have also has a lid on it with no large gaps.)
Do you have a heater for this tank? Generally, when bettas are kept in water that is too cold, they can develop fin rot.
Do you have any decor, plants, etc.? Bettas appreciate live plants - probably the best and easiest for a situation like this (even without a tank light) would be anubias. These are easily found in almost any LFS, and require almost nothing to survive. They can't be buried in the substrate, but merely tied to anything else, they will thrive. Some LFS sell them pre-attached to some driftwood, which might be the simplest solution.
Taking proper care of your betta will be a rewarding experience for your daughter (if she's old enough, you didn't mention her age), as bettas are quite the characters and have very unique personalities. Each betta reacts differently, and has distinct personalities.