Ronshar - Some of the school's around here have priority areas and out of catchment siblings are something like no. 5 on the priority list, after any in-catchment area child.
If this school is like that, I think it is very unlikely that you will win on appeal.
If your older child is already at the school, you must have a relationship with the secretary handling admissions. What has he/she said?
As Heated said, you must surely be very close to the top of the waiting list if you are that close to the end of the catchment. Do you know what number your dd is? A good appeals person will probably tell you that it is probably not worth appealing, unless in some way the LEA has not applied the admission criteria correctly (and it sounds as though that is not the case).
In which case, you would be best to persist in asking the admissions secretary how the waiting list is going and express your keenness for a place.
Someone is very likely to drop out over the Summer (before Reception starts). Often the parents will not inform the school or the LEA. The school then has to hold the place for a week, or something, before 'phoning down the waiting list. Most parents will have settled in their dc somewhere and will decline the place. Given your situation, you probably won't.
So hang tight, be nice and be prepared for a little wait and perhaps some disruption/inconvenience.