I do basic bike maintenance myself and my bike kit contains:
-Decent hand
pump for tires
-Bike tire pressure gauge
-flat repair kit- including tire levers, patch kit, and often also a new spare innertube. The self healing ones that prevent leaks on small punctures are worth the extra money
-a chain cleaner device, (an old toothbrush and rag works for starting out), degreaser, and chain oil
- socket wrench set and also adjustable wrench
- Allen key set (mine are all attached and look like a multitool, which means you can't lose pieces - probably a good idea for a kid, and also really convenient to quickly switch sizes)
-Multi screwdriver set
- hand degreaser for after I am done
You can buy bike stands for holding a bike on to work on them. I would love one if I had space, and could do a lot more tasks if I had one, aND some thinges a lot more easily.
Easyish bike tasks that i would suggest she learn are changing inner tube ( I learned while at university biking over lots of broken glass), cleaning and lubing the chain (at min, start and end of season, ideally more frequently), pumping tires, and replacing brake pads, and adjusting the brake cables. Before she sets off too far with her bike, make sure she knows how to get the chain back on her bike if it falls off somehow (walking home afew times with my first bike with real gears was not fun).