I would cook it, but I'm sure eggs are fine. A long time ago I asked the Vet what he thought about the BARF (bones and raw food) diet for dogs. He said he thought that nutritionally, it was fine, but that dogs are subject to the same food-bourn illnesses as we humans are. He said there is a reason we cook our food, which is basically safety. I said "What about wolves? They eat everything raw." He replied that they have no choice, they can't cook their food, and their lifespan is only about seven years in the wild. Big difference between that and the lifespan that dogs enjoy. The rule I've always used when "treating" my dog is never to give them anything I wouldn't eat. If the eggs are nice and fresh, and you are confident about their safety, then why not? I would cook it to be sure, but maybe that's just me.
I sometimes do the same, would not waste the fun of a raw egg by putting it in the food though !
Now & again I give the dogs a whole raw egg (in shell) on the grass they play with it for ages before eating it. Years ago my Dad used to do this with our GSD she would carry it around and play with it for a long time then when she wanted to eat it would throw it up in the air so it would smash on the ground. It's great to watch a dog given a new fun thing to do. ;D
ps - personally would not give raw egg more than once a week though