There is one photography tip that I would give any new mom (or aunt or godmother) photographer who wants to be able to take some better shots of her kids (or nieces/nephews or godchildren) that is very simple to explain and the results are instantaneous better pictures, regardless of the type of camera being used.
Here it is: Get low. Like, eye level low, when you photograph kids (or grown-ups, too, for that matter).
If your subject is a standing (or running), growing-like-a-weed 9-year-old boy, bend your knees a bit.
If your subject is a standing 6-year-old girl, you'll have to do a kind of deep-knee bend.
If your subject is a one-year-old sitting on her Daddy's lap, you'll have to do a squat -- the kind that makes your thighs burn after shooting for a few minutes.
If your subject is a one-year-old standing in the ocean shallows, you'll have to do a deep squat; and, yes, your bum may get unexpectedly wet.
The same goes for a the crazy kids zooming around the house on a plasma car. But, if your bum gets wet while you're shooting in the house, you've got bigger problems than I can help you with.
If your subject is the cute bottom of a standing baby or a little one crawling on the floor, you'll have to get really, really low. Sometimes I squat or kneel and then lean over to the side and get my camera as low to the ground as I can go. Other times I'll lay flat on my belly.
If I squat and lean or lay down typically depends on the what type of surface I'm dealing with (tile, concrete, grass, dirt, wet sand) and how much extra laundry I'm willing to do.
This is a belly shot (for both of us):
Give it a try. Focus on always shooting at your subject's eye level.
Whether you're photographing a nose-crinkling, tongue-wagging, rubber-band wrist, thigh-roly-poly, swinging baby...
Or a couple of cub scouts catching grasshoppers...
Get low and at eye-level, even if those eyes aren't actually looking at the camera.
Your photos will go from snapshots, to true photographs, in no time.