Most of the harnesses say to throw em out after like 5 years, so you're gonna be replacing it after a few years whether she grows out or not. I would consider a child size.
But adult small may work.
I've been using the Muddy Safeguard. It's pretty comfortable and they can be had for $80 usually and I have seen sales as low as $50 for the women's (same except the embroidery is pink not orange). It uses a carabiner to connect to the tree strap.
I'm 5'2" and 140# and I have an adult small. Even using it with just a tee shirt and jeans on, I am not even close to the minimum settings on it. It's pretty adjustable. The chest strap may be the limiting factor, I wear a 38S jacket and with just a tee shirt I am somewhat close to the minimum setting. My wife is close to the size of your daughter maybe a few pounds heavier and I suspect she could use my harness.
I think Muddy also publishes the recommended sizing based on height and weight.
I suspect with hunting clothes on an adult small would be good.
Hope that helps.
Last thing, the easiest and safest thing is the HSS Lifeline. Check it out. You connect in at the bottom of the tree, and your strapped in the whole time you climb, and hunt, and only disconnect when you reach the ground. It uses a Prussick knot that slides along on a high strength climbing rope that's tied to the top of the tree. Changed my whole view of treestand hunting. REMEMBER MOST FALLS HAPPEN CLIMBING UP OR DOWN NOT SITTING IN THE STAND!!!