No

"I don't see why I have to kill you." you reply. This takes the dragon by surprise. "The way I see it, I only have to defeat you to prove my self worthy of the princess. You could say that by finding the back door I have defeated the trap you set for me and therefore defeated you. Since you no doubt want to live I do not need to kill you there is no reason to fight. I also think that having a dragon as a guard dog is an excellent idea. Therefore, I propose a solution: You let me claim the princess as my bride. I become the ruler of the kingdom. In exchange, you get to continue living here and I will employ you as the castle's guard. Playing one dragon gold for it's hoard seams a lot cheaper than finding and hiring many human guards and is likely to be better. What do you say?"

The dragon thinks for a while then replies. "Ok, on two conditions: you let me take any livestock I desire as food without repercussions and let me have a mate live here too. I would very much like to raise my own family."

You consider the proposal and replied "I am sure that the farmers can be made to agree to keep you and your family well fed in return for the protection of a dragon from bandits and other monsters, like wolves and even other dragons. As for a mate, I am ok with it as long as they comply to the same rules and do not terrorise the kingdom or try to kill me and the princess. Do we have a deal?"

"Yes, but we may need to talk later regarding what might be required if I have a mate here but that will depend on the mate." Replied the Dragon