Since my first pool was an Intex 15' donut I'm right there with you. Mine was about 3700 gallons.
Watermom is right. You need some CYA in your pool. That way, you won't have to be adding chlorine all the time. While the pump is weak, I found it adequate enough to run a 4'x10' solar panel as well. Good care will allow you to spend more time in the pool and less time caring for it. But you can get a bigger pump and filter. Small combos are available from manufacturers like Hayward and Pentair.

Many trichlor floaters have adjustable vents so it doesn't over-chlorinate. I wouldn't recommend it for a donut though. You'll be tripping over it and that's not a good thing.

Carl