Well, if you'd aimed the camera a bit to the left, you not only would have avoided cutting off the hand, but you would have also put the baby's head off-center, which is generally a more pleasing composition. However, there are bigger fish to fry:
The background is out-of-focus, which is a good thing, but even so, the TV is so bright that it kind of commands attention and pulls my eye away. Always try to look IN to the viewfinder instead of THROUGH the viewfinder - it's so easy to concentrate on your subject to the exclusion of everything else, but our brains are good at doing that, and the camera is not. Learn to pay attention to what's behind and around the subject as well as the subject itself.
I would have rotated the photo a bit in post so that the table edge is level and the bookshelf in the back is vertical. Sometimes angled shots work well, but when it's close enough to level to look accidental it takes away from the shot.
This is another shot where it's cute, and it will be treasured forever, but it's still just a snapshot as opposed to a deliberate photograph. Your daughter is beautiful, and as a man with a beautiful daughter of my own I know how fun it is to get them in front of the camera, but for working on your photography I'd really recommend you find something else to practice on. I'm not saying to stop taking pictures of your daughter, but when you're emotionally attached to the subject it's really easy to just go, "Awwwww!" and completely miss all the technical things that are wrong. Practice on some fruit or dolls or landscapes or something, and then when you go to take pictures of your daughter you'll have the benefit of the experience from all those other shots.