Q-tanks are kind of a mess to mess with

.. just to sound grumpy, as waterdrop sometimes does, lol. Its just like you think, you need to deal with keeping your bacteria alive, or growing it in the first place, just like you are learning to do now on your first main tank. I got grumpy about it because I'm more like you now, just my son's tank and now his little quarantine tank, rather than like years ago when I had a whole basement full of tanks and having extra tank space or filters was not a problem.
People do it all the ways you could dream up. One of the most popular for people with a really big main tank is to simply be running a small filter of some sort on the main tank all the time that is switched over to run the Qtank on demand. A simple sponge filter (airline to a punctured tube running through the middle of a sponge) is very common or a small Aquaclear AC20 (or AC mini as that model used to be called.) The next most common practice is to simply take half a tray of media out of one of your big external cannister filters (feeling left out yet? lol) and stuff it into your dry AC20 which has been sitting in your dry Qtank inside a plastic bag in the garage.. that sort of thing.
Then there is the matter of keeping the bacteria alive while you run it. This of course is just like your main tank and all the skills you've been learning apply to it. What I did was to actually put a small amount of my mature media into my little ACmini (tiny HOB filter) hanging on the little 5.5G Qtank and then proceed to fishless cycle it. Every chance I got I washed the big filter in the little Qtank, making a mess, but cycling it fairly quickly. I then planned out a series of small stocking additions.
The stocking additions have been on the order of either 5 tiny neons, 2 or 3 slightly larger but small type fish or I would do 1 fish only if it was a larger fish. I put them in for at least 4 weeks but (and here is the IDEA, that I think is key) their real stay is often determined by my visits to my LFSs and when I see good ones that I want as the NEXT batch of Qfish, so that they can go strait in the same day that the old Qfish are transferred to the main display tank. That way I don't even have to take the cap off my ammonia bottle (but I would if I had to.. if I had a gap without fish and wanted to keep the bacteria alive for the next batch. If the tank reached full stocking and I thought I would not need the Qtank for a long time I would just dismantle it.
A trap to not fall in to is the permanent use of your Qtank. You can't believe how tempting this is! You have had to buy all the trappings.. a heater, filter, gravel, lid (I don't buy lights but just use a cheap table lamp I turn on before I feed them so they learn to wake up and eat, lol!) ..and of course my son loved the chance to decorate this Qtank... but you DON'T make it a permanent home for anyone or else you'll lose your Qtank and start having tanks littering the house! Then it becomes a hobby and... and...
~~waterdrop~~