Babies have a faster heart rate than adults because they are smaller.
Typically, small mammals have much faster heart rates than larger mammals. For example, adult mice have an average resting heart rate of around 500 bmp, adult males around 70 bmp and adult elephants around 28 bmp.
The reason is because the the smaller the animal (or person), the smaller the heart and the more work it has to do to maintain homeostasis in the body. This is because a smaller heart means smaller stoke volume per beat cycle.