10 years ago, I would have been totally with Snice on this one. In fact, much more determined. We had no car, had always lived outdoors, did hillwalking. I was convinced that my dd was going to be trained from an early age, she would learn to be out in the toughest of weathers and we'd be doing walking tours in Lapland by the time she was 9. It didn't work out. She walked late, she didn't seem to have any stamina, her legs ached, I ended up carrying her back from school.
Unfortunately, in dd's case, there was a medical reason: her joints were so badly hypermobile that she will probably never be able to do even a short day's walk. She needs a wheelchair to cover the 3/4 mile to school. As for bad weather, we now know she mustn't get chilled. End of dreams. It wasn't for want of trying.
Not saying that there is anything wrong with the OP's dd. Just that it seems early to beat yourself up about crap parenting. I'd have her GP give her a general checkout just in case.
Then I'd try to build up gently. Swimming is very good exercise for strengthening muscle. And gentle walks, gradually building up distance.
I do think it's annoying when people with cars tell you off for using a buggy (or in my case a wheelchair) when you're out on foot all day. What is a car if not a kind of wheelchair for fit people? And who is getting more exercise, the child who is taken straight to their destination by car, or the child who walks part of the way with a buggy for backups?