I own a Rossi youth .243 I purchased for my Daughter as well. The Rossi is not a tackdriver, but does seem to have "minute of deer" accuracy with most factory loads.
I don't recall the twist rate on the Rossi, but are you are shooting light enough loads so that barrel twist rate does not adversely affect accuracy?
The Rossi is rather light, so it recoils more than a heavier rifle would. This can affect a 10 year old, especially if she is petite and doesn't have much padding or mass to distribute recoil. I would not use full power heavy bullet loads when she is behind the trigger. You certainly don't want her developing a flinch this early in her shooting career.
I would recommend a PAST recoil pad of one type or another. There is one that slips onto/under the strap of a brassiere.
Here's something we, as guys, don't usually think about, but that my daughter learned from experience: If there is a little metal loop on the front of the brassiere strap between the Rifle butt and her skin, it can hurt a lot when the rifle recoils against it. The PAST pad prevents this, as does selecting the correct brassiere for her to wear.
I don't have an Axis in .243, but have one in .223 (have not shot it yet, still working on setting it up the way I want). The factory trigger may make it hard for a young shooter to be consistent. I would suggest you do a search on this forum and lighten/smooth the trigger just a bit. [Not too much; I do not recommend a really light trigger for hunting, especially for a youth hunter.] It's not difficult to do this yourself if you are mechanically inclined, and this will help keep your daughter from being prone to jerking her shots.
The biggest problem my daughter has is that she is petite and so holding the gun for any period of time is difficult for her. She has the strength, but it is harder for her than for you and I because she does not have the leverage advantage that we have since we are bigger and our bones are longer. She and I practice shooting from kneeling and sitting positions, and also using shooting sticks. She is still is working on getting the gun into position reasonably quickly and holding it for a shot when she is not using a bench.
Those are my thoughts and comments. Thank you for taking your daughter out with you. We need more girls/women hunting and shooting. I hope she enjoys it.