I've had the most success when preparing youth for hunts by taking them to the range over the coarse of several trips allowing them to try several calibers. At 13 they can tell you what they like and don't like AS LONG AS they don't have some perception that you expect them to shoot this or that. At 14 my daughter moved from a .243 to a .270 and I pressed her a bit to make sure she wasn't doing it just because dad shot a bigger caliber. Nope, she was just ready and wanted more energy at longer distances because she can and could shoot out to 500 yards in hunting conditions no problem. She knew her .243 dropped under 1000 foot pounds around 300 yards or so and wanted to make sure. (her own hunting rag reading) We built a semi-custom savage and she has been shooting that 6 pound light weight 270 ever since, my hats off to her. Funny thing is I shoot an 8 pound 25-06 because I don't like recoil much. All that to say, work with her, make sure she knows the options, make sure the rifle fits and she will probably use it for years to come. I would also recommend letting her try out a Lady Hunter or Camilla, those weren't around for me but they really do fit girls better and the stock specifically avoids perceived recoil...that helps make a better shooter regardless of caliber. Seriously practice shooting in clothes that are as thick as you hunt with and in non-bench positions unless you have a bench you hunt from.
6mm in .243 or 6CM or ??? Has worked great for at least 20 deer in the last 10 years using 85 to 100 grain hunting bullets of different types with 1/2 of them being between 250-350 yards. In close under 100 yards I've had bullets blow up on a shoulder and not make it through the other side but 100-300 yards seems to be the sweet spot. I've used soft points and BT bullets with similar results. At 350 we didn't get an exit on about a 200 pound white tail 1/4 away (rib entry, stuck on far side shoulder - shot off the ground)
We only have 5 or so deer taken between 400-600 yards but all with calibers and rifles that don't fit this conversation. (think tactical because we could)
I'm excited for you, what an excellent time you are at. I love hunting with my kids (who aren't kids any more) but be prepared, one day they will be on the 4wheeler heading out to hunt all on their own. I'll never forget thinking, they don't need me any more but really that means you've taught them well. Then the time in the stand is swapped with time around the campfire and all is well in the world once again.