6mm moose rifle?

At the ranges you're hunting I'd say go with whatever cartridge she's most comfortable making a flow up shot with if necessary. Going from a 77 grain tmk to an 88 grain tmk will gain you some penetration but I'm not sure by how much. Shot placement is the biggest key. 22 or 6 cal won't overcome a bad shot but either will work with good shot placement and a heavy for caliber bullet. Good luck and don't overthink it!
 
get her a 243 or 6cm and have her shoot lightly loaded 68 or lower bullets so she's confident. Then on opening morning, load the rifle with some medium/high powered 90gr ballistic tips (that you've zeroed privately) and she won't feel the difference when shooting big game.
 
Sub 100 yards, something subsonic and 35 cal+, say 350 legend thru 45-70. Will be quiet and recoil is low enough that I shoot those in a handgun. I have used the 205 makers in a 360 bh. Amazing performance. The 45-70 500g’s from maker are excessive penetration, but they are offered in lighter weights for less recoil and penetration.

Shots over 100, then 6 arc.
 
I'm thinking about all this.

First, shot placement trumps everything.

Second, I seriously doubt if any of the cartridges your daughter could shoot would give an exit wound. A 308 didn't and a 358 Winchester with premium bullets didn't. So I would NOT jump from a 6mm ARC to a 6mm Creemore thinking it would do significantly more damage to the moose. All these bullets will get through ribs and trash lungs. I doubt any will consistently exit. Shoot what she is comfortable with. There is no low recoil round I would try a Texas heart shot with.
 
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