Oh, Hi there! My advice is to let your quaker settle in for quite a while first. As far as introducing him/her to other animals, it depends on what animals and whether they are safely separated and supervised. I would, under no circumstances, let your quaker be in a room free to roam with a dog or cat, as this (in my opinion) is a recipe for disaster. However, you could place the cage in view of the other animals (at a safe height) so the bird can see the other animals. ALWAYS be present to supervise.
Anyway, that's just my opinion. Others may differ. All the best.