what social skills targets are on her iep?
what social skills interventions have school tried so far? (there are a lot of programmes etc available now)
essentially, wihtout a statement, dd is not guaranteed to get the support she does now. does she have any 1-1 support?
depending on the outcome of statutory assessment, school might get a little more funding to allow them to support her, and it will also formalise the support she gets.
do you have input from nas? if you or the ep suspects that she might be on the spectrum somewhere, it would be useful for school to know that. they can then access more respurces that might support her better.
fwiw, we didn't bother getting dd2 statemented until she was due to start school. nursery provded 1-1 etc and it was all fine. but for school age kids, i do think that if their issues are not going to go away, there is something to be said for safeguarding them/
i would also suggest you concentrate on what you think will happen with transition to secondary.
will dd cope without some 1-1 support? moving from classroom to classroom, attending different subjects (without a freindship group?)
often there are so many statemented children at secondary and so few support staff, that children on sa or sa+ are very much 'also ran'. school are aware of them, but they do not necessarily have the resources to do much for them. the support goes primarily to the statemented children.
in a smallish primary she is coping. would she cope in a larger secondary?
it will be much easier to get the stat assessment done now and in place prior to transition (and will mean that her support is in place before she gets to secondary, rather than it taking a year to get sorted if she can't cope when she gets there).
the as/asd thing is an interesting debate. most people who are vehemently anti-dx at the outset do decided that the benefits outweight the concerns, eventually. but it's v personal.