The first thing to ascertain, as PP have said, is whether this is an Infant Class Size appeal. If the PAN is 30, a multiple of it, or a number that allows classes in YR/1/2 to be 30 (so a PAN of 20, say, allowing 2 classes of 30 over the 3 year groups) then it will be ICS and thus exceptionally difficult to win, as this is the legal maximum normally allowed. An appeal for ICS can only be won if the LEA made a mistake that cost your child a place, the admissions criteria were unlawful, or the decision not to admit was legally so perverse no regular person would have made it.
In the case you describe, that sounds unlikely - you moved late, and thus were simply put on the waiting list for a full class. There is a very limited amount that could have gone wrong there realistically, especially if you have been told you are first on the list and no-one has left the school since. The child joining the class is likely to have an EHCP that names the school; assuming that you're happy that no-one has left and this child hasn't got the first place from the waiting list by mistake, then grounds under ICS seem very unlikely.
If the PAN is not 30, then the appeal is on the balance of prejudice; you need to show that the prejudice to the school of admitting would be less than the prejudice to your daughter of not being admitted.
Quite frankly, if the class is already 4 over PAN then I can't see a panel would be happy to admit more unless there is some strong mitigating reason why the school can cope with so many more than PAN (it has spare classrooms and teaching staff for some reason, say, which is basically very unlikely!)
There is no harm in appealing, and you can appeal once per academic year; but on the face of it, there are no grounds here for a successful appeal I'm afraid.
(I sit on appeals panels BTW)