I concur with the questions above. Unless your daughter is an accomplished shooter, having her use a rifle with a strong kick could potentially cause her to 'fear' the gun and develop a flinching issue.
I would recommend a Marlin 30-30 as a starter rifle. In a couple of years she can move up.
When I took my daughter to the range for the first time, I started her with a .22. It took about 10 minutes for her to feel comfortable and ask, 'what else do you have?' We then worked our way up through 9mm, .40, and then .357. (didn't have anything larger at the time). Not bad for a 5 year old (okay, she was 15 )
she has t/c 223 and 243 rem 7400 rifle that she used last year deer hunt in Missouri she know how to shoot rifles ok. I`m just getting ready for Indiana deer season hope this year or next
Standard pressure .45 Colt 250gr SWC will go completely through a deer, and there's no need for more recoil than that, so that would be my recommendation. Add to that the velocity increase you'll get from a carbine length barrel. The 250gr XTP is also a proven bullet, both in .45 Colt loads and in muzzleloaders w/sabot.
Don't forget about the single shot H&R in .45 Colt.
.357 Magnum is also an option in a lever gun, which makes very cheap plinking reloads with .38 SPL possible. Then use 158, 170, or 180gr deer loads (a 170gr SWC or the 180gr XTP would be my preference).
I stated both my sons out shooting bolt actions....in my case a Marlin .22.
In my opinion I think that a bolt is good from a safety standpoint because you can control the ammo and the kids like to work the bolt and it is safer especially if you start from a bench since they don't have to lift the gun and move it around too much to work the action.
I also chose the .22 in order to keep recoil at a minimum...I heard too many stories of guys who started kids out with too big of guns and one good thump from the recoil and they were done for a long time if not forever.
Safety is the first concern...invest $100 in a good used bolt action.22 and let them have fun and move up to bigger calibers at their pace. Don't force the issue.....
My kids broke in a Rugar 10/22 with countless thousands of 22lr. We also picked up an inexpensive 22lr revolver that they can shoot better than I could ever. I like the inexpensive nature of the ammo and the 10/22.
she has been shooting 22lr rifle and 22lr pistol for last 2years
and she also member of 4-H club(shooting sport) 22lr and archery
and deer hunt for 2years with 2deer some times she will out shoot me
I've been thinking of a .357Mag Handi-Rifle for my boy of same age. I figure get him used to .38s in it and work up to full-house mag loads. Once he's comfortable/proficient with that, ream it out to .357Max and he should be set for deer season.