Not a recommendation for the whistle pigs, but we set up my niece and nephew (12 and 13 at the time) on a Handi in 30-06. Limbsaver recoil pad, and a stock that fit them. Started them on a reduced load Remington round, and I had reloaded some 130gr light loads. They shot those and had an absolute blast, ran out of those that day, and wanted to keep shooting, so they started shooting the reloads my brother and I were shooting, 180gr full house loads we use for elk (not quite maximum W-760). They shot those the rest of the day, and had no issue at all with them. Cool thing, now when we hunt, the four of us carry the same reload. I also agree, always, always give kids hearing protection. I have a notch in my hearing because I never used protection shooting a .22 and .223 when young.
Anyway, talk to the 11yr old and let her shoot some of yours if they fit her. I have come to the belief that fit and a recoil pad will make the biggest difference, especially with kids. Also, what are you and your friend shooting? Would she feel more comfortable happy with the same? Would it be nicer for all of you to have fewer calibers on the hill?
BTW, they both love to shoot my Marlin in .44Mag and .357Mag.
--Carl