It seems odd that she's only giving you forms to sign now. IIRC the usual procedure is that on each headcount day (a specific day towards the beginning of each term) parents are given a form to fill in and sign to say that they want their child's funding to go to that nursery or to two nurseries if the child attends more than one. (eg 3 sessions of funding to go to x and 2 sessions to y). The form is handed back straight away and sent off.
I think that the funding only comes in 2.5hr 'blocks' though so if dd attends for 1.5hrs it is automatically rounded up to 2.5hrs. AFAIK you can only apply for the coming term and not have it backdated. I've seen a few children miss out on funding because they started nursery a couple of weeks after headcount day. If dd has left the nursery you shouldn't be signing anymore forms for her. The last headcount day was just after the Easter holidays and the next one isn't until September.