Walking with a sleepy Dale is like walking with a drunk person and he hoped that the Alpha wouldn't get drunk in general, if his mere sleepy state was this bad, he couldn't imagine how bad it would be when he got drunk.
There were advantages to living all alone on the fourth floor, creepy as it seemed, it meant no one was here to see him struggle with Dale's bigger form.
He had half the mind to just let Dale drop to the ground and start to roll him down the hallway… what? He was exhausted too.
But somehow he managed the trip to Dale's apartment, relieved that he at least knew where to go, the door was unlocked to Dream's chagrin… he would scold the Alpha again as soon as he was lucid enough to understand his harsh words.
He pushes open the door, locking it from within on instinct and continuing his lumbering journey to the Alpha's bedroom, he just makes a wild guess.
It also helps that the two Pack House's were designed similarly.