Frankly, I would recommend a new shopper leaves kids at home. At least until the shopper is really, really comfortable with shop requirements. Even adults, who know exactly what you are doing, can screw up a shop ROYALLY.
At least for the beginner, I would recommend scheduling around hubby's work schedule.
Possible shops to take child: drive thru fast food. I can't believe that's the only one I can think of, but it is.
Companies to be sure to sign up with: Marketforce, The Source (grocery stores) (kids NOT allowed), Maritz (gas station mystery shops; doesn't pay much, but we all need gas; and the mystery shop ones, well....I couldn't leave a kid in a car while I went inside, but some people don't have a problem with it).
But I'll be watching this thread, because I'm about to take on child care for my 2 month old granddaughter, and if I can find shops I can take her on....I'll be happy!!!!