It all depends upon how much light is available.

If you use the flash for the pictures, it will require a few seconds (2 or 3) between shots.
The flash circuit has to recharge the flash capacitor before the next shot.
This is true for any camera.

If you set up photo flood lights, you can shoot as fast as the camera can cycle, which can mean 4 or 5 shots per second.

If you shoot with available light (without flash) it depends upon how bright the area is.
If the baby is active, you will need a camera with a bright lens.
Something like the Canon S95, Nikon P300 or Panasonic LX5.