Call the school and ask. Not all schools run on a quarter-schedule, so there is no noticeable break in subject matter. Also, schools often cover materials at different paces and/or in different orders, so the earlier in the year you can transfer schools, the better to prevent a gap in subject matter your child learns.

Your best bet is to call the school directly and ask. While the end of a quarter is often a midterm grading period, you might find certain teachers will be continuing on with previous lesson topics, and the sooner your daughter enrolls, the more familiarity she'll have with their subject matter. (For what it's worth, my child's school already ended their first quarter more than a week ago....)

I don't know what state you are in, but typically quarters run 45 days.