Illegal / dangerous to pull 11,000 trailer rated 10,000 lbs?

It is illegal to go over you gross weight vehicle rating. It is unsafe for you to go over the GWVR. If you are in a collision and they figure that out your screwed. If a commercial vehicle enforcement officer figures out your over GWVR he will put you on his portable scales and find out how much and probably give you a big fat ticket for it. Probably not a high chance of that happening though. So its like swimming when there are no life guards, at your own risk. I'd say get a vehicle that will pull the trailer you got.