I've moved this to Appeals which is where we advise on specific cases.
The intention to move house is worth a brief mention, but is unlikely to carry much weight because the rules have been correctly applied.
All that matters will be your reasons for preferring the school
In addition I will add all the trophy's she has won at her current school and include all school reports and commendation letters she received.
None of this will be relevant unless it supports your reasons for wanting a place. As scary mum suggests, it's a waste of time setting out to prove ability when your daughter has already qualified!
I can see the relevance of a trophy for maths/science.
And of a school report where she's described as "a brilliant mathematician/scientist
(Schools are no longer funded for specialisms, but no doubt they have some residual expertise.)
Please read the Q&As if you haven't already done so:viewtopic.php?f=35&t=35032
Good luck with the waiting list.