I would make the bow about two of three inches longer than your daughter is tall.
Four year old kids grow like weeds you know. This will give her a bit of growing room with the bow.
Put a 4" stiff handle on it. Make the handle about 1" wide. Do not flair the limbs out at the fades.
Leave the limbs 1" wide half way to the nocks. Then taper the last half of the limbs down to 1/4" tips.
Put some kind tip overlay on it. Most anything that is hard will work for overlays. Cut your string grove (mostly) into the overlay
instead of the sides of the tips. This bow will end up being wafer thin. So go easy on the tiller. You will have little room for error.
I have made about 25 or 30 of these. They are fast and easy to make and the kids love them. Parents.... Well, I have learned
to ask before handing them out.
David