I'm four foot seven and 72-73 pounds, probably near the size of your daughter. I've never used a .243 or a 7mm-08. But I have no problem with the .30-30. I have a recoil pad on mine, but there doesn't seem to be a lot of kick.
We have two daughters, nine and six. They go out hunting with us and know more about hunting and shooting than a lot of grown men I meet. The only reason they don't hunt is because they take after me and are way too little to effectively handle a gun or bow suitable for hunting. They are great fishermen though.