If I think there may be another party on the same day, what's a good time frame for sending out party invitations?

My pre-school age daughter has a birthday end of May. I started calling party places in February to get ideas and prices. It was unbelievable that the place I wanted, a place with the best price, was already booked for most dates and times for May, except the undesirable time (Sunday night at 7 pm – a lousy time for a pre-schooler’s party). So I went into June, and booked her party for June 18. I put a down payment down for this date. (and now I know that next year, in order to book a May party, I need to start calling in December – believe it!).

I got the class birthday list from the teacher, and see that there’s one kid with a birthday June 19 and another with a birthday the following week. Therefore, there’s a good chance one kid will have a birthday party scheduled the same day as my daughter’s.

What is a good time frame for issuing invites to this party, in order not to put them out too soon, but yet to inform any party planners that this date is booked? Of course, each child would invite the whole class so this impacts all the kids in the class.