No comment on your tow ratings, but a comment on your driving license.
You may be able to get away with your current drivers license, you may never be questioned. BUT, if you are ever pulled over for a traffic violation, be involved in a traffic accident (no matter how minor), law enforcement will be inspecting your drivers license. I don't know what the law says in your area, but I wouldn't want to risk that!
If you get the camper, do the right thing and get the proper driving credentials too.