I would not let her shoot the 308 Years ago, the wife was tossing skeet for me one afternoon and asked to shoot my 870. Told her it kicks but she insisted she could handle it. So, figured what's the harm, she'll either handle it or not. Well, she barely handled it. But now, years later, she'll can only shoot a 20 ga When she tries the 870, she flinches, has the yips just waiting for the kick.
Start her on a 243 and work up to the 308. She needs to learn the proper form and technique, not thinking about the recoil. Do you have any Rifle ranges, firing lines, or clubs around? Call them and ask if they rent guns. I'm sure they would be happy to help your girl out.
Have fun, sounds like you have a cool kid.