Is this a normal behavior for a dog?

It is totally normal. You have nothing to worry about here. Weenie dogs especially tend to gravitate to one kind of toy or one favorite toy. At the last vet clinic I worked at, we had a regular boarder that had a blankie and he would suck on it to go to sleep. Otherwise, he was an awesome, normal dog. My dogs favorite toy is his Extreme Kong and he will spend literally all day playing with it if I let him. I wouldn't worry about your baby too much, he sounds like a great dog!