Yes, people have sucesful appeals, but they seem to focus, at Reception stage, on a mistake being made that denied the child a place. Do you think a mistake has been made?
The distance from school can be misleading. In some areas, it would practically guarentee a place at a school. In some areas it may be 0.6 miles too far.
Did you put any other prefered options down on your application form? Are there any other schools in the area you would prefer instead of your allocated school? It may be worth going on those waiting lists also.
My Son didn't get a place at the nursery school he was at (we knew it was a high risk, but the logistics worked for that year), and so started in YR with 89 kids, of which he knew a handful. He has made loads of new friends. At that age, friendships can be transient, so I'd reassure your daughter that she will meet lots of new friends, and if the others live close to you, she can still play with them evenings and weekends.
If you do end up with the school 2 miles away, could your daughter bike or scoot?