Sounds like a youth .243 would be the ticket...

Don't worry about off hand wobble, good marksmen learn to take a rest in the field...Learn to squirrel hunt with a .22, after awhile you learn to stop by a tree, there's your rest...

Most deer hunters use a bolt action rifle they are more accurate, the action is stronger and the trigger can be easily adjusted...Stick with the bolt action .243...I've had mine since 1980...