be warned, if you spend lots of dosh to get a "faster" f2.8 lens you end up with a much narrower depth of field, especially close in to the subject, so then you'll need to start a thread "Blurry stationary baby arms and legs issues "
I dont know exactly how your camera works with it's flash, but I suspect its not dissimilar to the TTL functionality on my canon 400D.
So put the camera in manual mode with TTL (or whatever its called) flash , you then have full control of aperture and shutter speed to suit your subject, so set shutter to freeze the limbs (say 1/125 or 1/150, dont exceed the cameras max flash sync speed although it probably wont let you) and use f8 or f11 to get decent depth of field as limbs tend to get waved towards you (shorter depth of field towards you). The flash will probably (if it works anything like mine) then get adjusted automatically to provide the light necessary to suit your camera settings
If you are worried about direct flash power on the baby try it on yourself first, with a helper, or in a mirror with camera on your shoulder
If you want to try diffusing the popup flash there are all sorts of methods: pieces of white paper or kitchen foil can both be used as reflectors to send the flash onto a convenient white ceiling, or plastic milkbottles cut up to fit as diffusers. You'll lose a lot of power with any flash modifiers so it'll be slow to recharge, and you may max out the flash power, if that happens increase the iso until you get to the point you need a seperate flashgun
Dont forget you can mix flash and daylight to improve lighting, a strategic window may not be enough on its own but combined with a popup flash may make it work.