There are many, MANY nannies who are currently working with a nanny family, but are looking for a better fit. They can't afford to quit without another job lined up, but are still contractually obligated to give their current family 30 days notice. I always recommend starting the nanny search 8-10 weeks in advance to give ample time for multiple interviews, background checks, reference calls, contract negotiations, trial days, and time for nanny to give notice to her current employers.
Even after all that, ideally, there is still a 2-3 week buffer, just in case it doesn't work out with your top choice, to revisit one of the other candidates, hopefully with enough time to do all of the aforementioned (background check, contract negotiations, trial day) before the date which you absolutely need a nanny to start by!