Our school run (1.5 miles) is up a steep hill, and includes quite a few steps, and a footbridge that has no ramp. It's a nightmare with a buggy.
At your DD's age she'd occasionally do the school run x4 (plus some other little bits) on her own steam, but it would include a scooter or balance bike. More usually we'd do one of the two legs by bus. Now at 3 and a half, she did it on her own pedal bike on three consecutive days, so 2h on the bike every day and did over 9 miles.
DS as the eldest started school at just four and scooted there and back in the first year; sometimes walked. Other parents thought it was amazing but it really just is what they're used to.
Yes it takes significantly longer than if I'd transport her in some way but I don't see it as lost time. When it rains we dress up in waterproofs and have fun in the puddles. It's our outside time and exercise time. Saves me taking her to the park and boring myself watching her climb up and slide down the slides.
I wouldn't recommend exclusively walking though. A scooter is great as you can easily keep up with it without jogging, but especially as you can have a tired tot (or simply a refusenik who won't take another step when you're rushing to avoid being late) just stand on it whilst you pull them along. And it is a lot faster than walking at toddler-speed.
If you eventually switch to a balance bike, you can have the whole family on bikes by the time DC2 starts school.