I am an MB and may be wrong, but from my experience you will get more applicants for the beginning of the school year because career nannies often stay with families for years until the last child goes to school or longer. However there are always nannies looking for jobs, their employers may have moved, they may have been hired in September by a crazy family, etc etc. that being said, if you can't afford to hire someone until you go to work you could interview applicants in the Summer who many be willin to take temp jobs until your date if your family is the right for for them.
Forgive any typos, I am typing from a phone.