YES! Don't worry, the earlier they catch it the easier it is. They just carry on pretty fine and the spots dont seem to bother them so much when they are young.
My little girl who's two and a half has it just now and so far my nine month old son doesn't have any symptoms but i've been told that he may develop it and I have breastfed both of my children. Don't panic if your baby does get it though because as phae says , it's better they get it young as i have heard it can develop into shingles if an adult catches it in later life and it can be linked with infertility problems in men.