Of course it depends on the child, but in general yes, 1.5 miles each way is well within range physically. Terrain is also a factor, so if it's all uphill in either direction you'll have to make an adjustment. One approach would be to do local circles and see what her comfort range is before doing a 1.5mile out and back.

As to the bike, kids grow fast so there's good turnover in nice used bikes. Going that route, you could come in and get out for small dollars when she outgrows this bike, vs. taking a good sized hit on a new bike. Though it isn't common, some shops will work closely with you allowing you to trade up for smallish added dollars as your children grow.

BTW- congratulations on taking the plunge and moving to a carless life.