Earlier, Harley and Superboy-Prime had flown past from afar on an enchanted cart. The Adjutant told Constantine who was on that cart, giving him a basis for deduction.
He remembered that the monster outside had gone quiet for a moment. It had actually been reading the passersby's minds, trying to alter its form.
It had failed because Harley had Tenth Metal stuck to the back of her head, and Damian had the same. Superboy-Prime was protected by his Bio-Field, Raven's mind was shielded by Trigon, and Doom Patrol was a bunch of lunatics.
On top of that, they had been moving too fast for it to hunt them. So the monster had not pursued them. Instead, it stayed here, continuing to make sounds like knocking and stifled giggling, luring the people inside to open the door.
Simply put, the things it transformed into were things that interested the people in the house.
The monster was invisible because Constantine called himself Hellblazer. He often dealt with demons and ghosts, and he enjoyed investigating cases for money, so things he could not see naturally interested him.
As for why the monster's vague outline looked somewhat like a dog, that had been a misjudgment caused by its blurry shape. It should actually have looked more like a rabbit, because rabbits were Little Zatanna's favorite animal.
The first trick she had learned as a child was pulling a rabbit out of a top hat. That animal held special meaning for her.
After the Farmer Squad had been sent over by the Adjutant, the void monster began reading their memories as well, taking on forms that interested them. But there was no way to match up exactly who liked tentacles, who liked spiders, and who liked spines.
Constantine knew these people were all classic horror