Me too -- I was very worried about this on our first cruise when our youngest was 5, a climber and jumper since the day he was born! Would not have gotten a balcony except DW insisted on it. But of course everything turned out fine.
A warning though: be SURE you know how to lock the balcony door! I thought I did, and I was wrong! There were no instructions in our room for how to lock it. If you don't have instructions, ask your cabin attendant to provide instructions, either printed, by showing you how, or both. And each time you think you have locked the door, test it!