You really think that .020" more bullet shank diameter and 31 grains of bullet weight is going to matter when you're going to guide the user into shots of 200 yards or less?
Do you also think that a broadside elk is really more bulletproof than a broadside mule deer is?
I've tagged 20 elk in my lifetime. The farthest I've ever shot one was 178 yards. I tagged 9 of them with a .30-30. I tagged 7 of them with a .270 Winchester. I tagged 1 with a 7-30 Waters from a Super 14 Contender pistol. I tagged 1 with a .257 Roberts. I tagged one with a .495" patched round ball from a .50 cap-lock Lyman Great Plains muzzle-loader. I tagged one with a .250 Savage, a round slightly less powerful, on paper, from 200 to 300 yards, than 77gr. 5.56 NATO loads from a 20" barrel AR-15 are.
The 100 grain Nosler Partition .250 Savage handload I used got an average MV of 2620 fps out of the 20" barrel of the Ruger M77RL Ultralight I shot it out of and was loaded to SAAMI pressure. I mention this because the terminal ballistics of that ammunition from that rifle aren't substantively different than my old 70 grain 5.56 NATO handload delivered, and the 77 TMK 5.56 NATO load I've been using since last November makes higher volume wound channels, more like what I'd get from a 160 gr. FTX launched at 2370 fps from my Marlin 336 in .30-30, or a 120 grain Ballistic Tip from a 7-30 Waters fired out of a Contender pistol at 2,400 fps from a 14" barrel.
No animal alive is going to live on whatever minor terminal ballistics differences that exist between the 5.56 NATO, .250 Savage, 7-30 Waters, or .30-30 loads previously described.
If you shot an elk at 200 yards or less with a 6mm Creedmoor I have a hard time believing that you or the elk you shot would notice a difference if I hit it in the same spot with any of the 70 grain to 77 grain 5.56 NATO loads I've used to take game with. If you drive a bullet from either one into the same spot on an elk at 200 yards, you should get the same result out of either of them.
Opinions are like colons. Everybody's got one.
Mine, as a former licensed and bonded hunting and fishing guide in the State of California (#2725) is that I would rather see your daughter show up on a Central Coast pig hunt with the rifle and caliber that SHE is comfortable with rather than the rifle and caliber her father is more comfortable with. She's going to be a whole lot more comfortable shooting 77 grain TMKs from a .223 Remington / 5.56 NATO than she will be shooting 108's from a 6mm Creedmoor. As a guide, it would be my job to get her set up on a shot that she's comfortable taking and that will result in a clean kill from the rifle and ammunition combo she's comfortable using.
I've literally seen thousands of wild pigs get shot. The key elements to deadliness were plenty of practice, away from a bench and rest, from field positions, with the same rifle and ammunition going on the hunt. The cartridge, from 5.56 NATO on up, fundamentally had no bearing whatsoever on the outcome. Placement was key, followed by penetration, Once we had .224" bullets designed for medium game, my experience was that inside of 200 yards, everything from .223 Remington / 5.56 NATO and up kills game just as dead, because they all have the capability of shooting completely through a pig's chest cavity at 200 yards with the correct bullets. Mono-metal bullets out of the pipsqueak .223 / 5.56 have the capacity to break a 302 pound boar's shoulder blades at 237 yards. A pig with two broken shoulders is a stopped and soon to be dead pig.
It's not really about what YOU feel comfortable having your daughter take game with. It is about what SHE is comfortable taking game with, coupled with whatever method of take restrictions are in place for the game she's going to take.
That's a reason to move her up to .244," .257", or .264" bullets, IMHO.
I doubt I'll ever tag another elk. The last one was all shits and giggles, right up to the time the hammer on my old Marlin 336 hit the firing pin and there was no stopping the 160 grain FTX bullet from exiting the barrel and center-punching that bull's heart. What happens after tagging is no longer fun for this old man.
If I DO buy another elk tag, it'll be for the same place I tagged my last one in four years ago. I won't be buying another rifle. I'll take my AR-15 A4 in 5.56 NATO and fill my tag with that, or have a ball attempting to. A Ruger American Gen 2 in 6mm Creedmoor, or the lack of one in my case, isn't really what my success, or lack thereof, would hinge on, and it wouldn't be for your daughter, either, if she gets plenty of trigger time on her .223 with same ammo she'd be hunting with.
