I think I'd step up to a slightly heavier velocity, bullet and gun.
Just thinking out loud.....
25'06 is a flat shooting, low recoil round
300 savage is a comfortable round
257 Roberts is low recoil
6mm....
260.....
There are better alternatives to the 243 when going after deer; but the 243 will do the job when the shooter uses good placement and premium bullets.
I'd go with the 6mm or 25'06 in your shoes and in a varmint barrelled heavy rifle with a good quality scope and aftermarket recoil pad. I think Savage offers an entry level priced rifle that will provide all that for a fair price (I'd opt not to purchase a scope package with savage and spend all I could afford for top glass.)
<EDIT> Have your daughter practice with both in-the-ear plugs and muffs. Recoil often get mingled with muzzle blast in the mind. Also have her practice with a 22lr. A 22lr is the best training tool in the world!!! I'd have her shoot at least a box of 100 22LR for every box (20) of centerfire cartridges.
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