The recoil isn’t what’s getting her. The noise is. I cannot put my finger on what precisely the problem is for her. But I’ll damn sure do what I have to to make sure she has a good time.
She hunted with Xbow a few times and as she grew older the .243 didn't bother her. I think that Xbow would be more readily available and easier to buy/sell (even used) than airgun but whichever you pick, jump on it and don't look back. Not worth missing out on a hunt with your kiddo! Have fun with her.
If it makes financial sense I'll ship you our daughter's Xbow for your hunt. For that matter I'll check with our daughter and maybe we're ready to pass it along to someone else as she'll probably graduate to bowhunting when she does something besides rifle now.