Let her handle and shoot both and choose for herself.
The .243 is fine for many types of game but if elk are on the menu I'd start her with the .243 and work her up to the 7mm-08. I would also consider getting a a youth or compact stock if it would fit her better.
Coyote Hunter - NRA Patriot Life, NRA Whittington Center Life, GOA, DAD - and I VOTE!
No, I'm not a Ruger bigot - just an unabashed fan of their revolvers, M77's and #1's.
A good .30-06 is a 99% solution.
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