There was an interesting article in a gun mag about designing the perfect rifle cartridge combo for just such a purpose. They ended up with a Browning BAR ported for the .416x338 cartridge.

I wouldn't go below a .270 and the 9.3x64 gets a lot done without intolerable recoil. Hal Waugh would carry a .358 Win. carbine at times and the .350 Rem Mag could certainly and has got her done.

So get her used to something 30 cal. or more or get a nice camera. A 308 Winchester at close range is just as deadly as a 30-06 at 100 yards further out. Use a good bullet and there should be no worries.

"When you disarm the people, you commence to offend them and show that you distrust them either through cowardice or lack of confidence, and both of these opinions generate hatred." Niccolo Machiavelli