No, I can't imagine that it is grounds for appeal at all. The fact that she has qualified doesn't mean she's guaranteed a place, and unless the LA made a mistake (which it hasn't), then the waiting list is the only viable option.
@Alexa0909 whereabouts in Bucks have you moved and was the allocated school a grammar?
The places are competitive, but mainly due to out of catchment children taking places.
You are (or at least should) be high up the WL as you live nearer than any others on the WL, so have a fairly high chance of getting a place, as the others will be qualified children out of catchment.
The only problem is that places are rarely surrendered, usually only for moves,cas no one is likely to give up a grammar place unless they move.
Depending on where you live, there may be more than one grammar close,cos that gives you more options.
Would the council pay for transport to the original school in the interim? I know the rules say that they pay for transport only to the nearest school with places, if it is over a certain distance, so usually you.wouldnt be eligible if you choose a school further away and there are closer ones, but when you applied you were within catchment, but have moved and they now have no spaces nearer, so it's worth enquiring.
Even a move into Y8 isn't a disaster, several girls moved into DD"s school in Y7 & Y8 (in Aylesbury), so there is movement.