monkey I'm not generally a judgey person, but I'm afraid I would be very shocked by a reception age child arriving at school in a buggy, and you only have a 10 min walk.
Reception class in my child's school a month in they start walking to the local shops and library occasionaly, tied in with lessons, that's a good 20 min walk then the same back, never would it have occured to me that the children would not be able to walk that far at that age, it has never been an issue at all. Reception children have an all day school trip at christmas, again they are on their feet pretty much all day, lots of walking, parhaps you need to address this, before it starts causing problems, as the teachers will expect her to walk.
Does your daughter have medical issues? Is it just walking 10 mins to school she has a problem with, would she be fine if you were walking to the park? If no medical issues, than I'm sorry it's a parenting issue, you need to take control and tell her to get on with it frankly, she is walking, end of, as I say needs stronger parenting.
taffe the "lets walk 5 miles each way in a howling gale, brag loudly about to all and sundry, anyone that doesn't is raaaaaaally unfit " make me puke
nobody is suggesting that, completly irrelevent, we are talking about a short 10 minute walk to school in monkeys case.