Last year, when the winter finally broke and we had a gloriously sunny spring day dh and I, with ds napping in the stroller walked 4.5 k (I think that's around 3 miles) to dd's school, picked her up, and walked back. She was 5yo. It was no problem whatsoever.
Usually we drive back and forth from school (we carpool with 2 other families in the neighbourhood), but besides that barely ever use the car. Even in the coldest days of winter (and it gets COLD here) I'd say we walk a minimum of 30mins a day (15mins each way to the grocery store). On good days, esp in the summer, we walk for hours. Ds is 3yo and still spends some time in the stroller if it's a really long walk. Dd is 6yo and has no problem keeping up with us.
OP, I think it's great that you get that much walking time in with dd. I loved walking to and from school at that age (it was a little closer... I guess 1.5 miles).
Biking is great too (dh plans to start taking dd to school on her bike starting in spring... her best friend and his dad biked to the same school from a bit farther starting in K). OP, since you mention you have balance issues, have you thought about getting a recumbent trike?