This is not a short process. The sd has 60 days to perform the evaluations. I can't remember right this red hot minute, but I think they still have an additional 30 days to write the report and hold the eligibility meeting. If you can get your request in quickly, it might just work out to have the IEP eligibility meeting just prior to school starting in the Fall.
Be sure and send the request via Certified Mail. The CM starts the clock ticking.
However, if your district's administration office is open during the summer, then it is reasonable to expect that you can get the process started now. If school is already out (or will be out shortly) and the Administration office is not open during the summer, then the evaluations can't even begin until the Fall Semester.