When should I tell my new employer that I am pregnant?

When do I tell my new employer I am pregnant?
I have been working as a nanny for about five years and was contacted at the end of July by a family who was looking for a nanny for their newborn son due on Labor Day. I went for the interview and was offered the position at the beginning of August which I accepted. We signed a work agreement on August 17th with a start date of October 3rd. About a week after signing the contract, I found out that I am pregnant. I am supposed to start work in less than two weeks (I'll be 9 weeks pregnant at the time) and I am not sure when I should inform them that I am expecting. I would like to work for them right up until I am due at the beginning of May and then return to work after a short maternity leave. This job is the nanny job I have always wanted (On the books, Paid holidays, Paid Vacation, Guaranteed hours, etc.) and I don't want to compromise it. I was thinking about telling them about a month into working for them at the end of my first trimester but I am open to suggestions. When is the best time to let them know and do you think they will want to find a different nanny? All feedback is appreciated.