I would say that every single nanny has an age range they prefer to work with. For me, working with school age children doesn't feel like work at all. If I was given a baby to look after I would strive to do a good job, however I wouldn't love what I was doing.
In this financial climate (where there are far more nannies than there are jobs) you can afford to be fussy. There are plenty of nannies who LOVE to work with toddlers, and looks like you've already found one who loved working with babies