Cats may not get along well with other cats at first, let alone dogs.
Keep them seperate at first, they can sniff each other through the closed door. Gradually allow supervised contact until they get used to each other.
Not sure its a disadvantage to have the cat somewhere else, like someone said, they're territorial, it might be better to have both of them meeting on unfamiliar ground, i.e. their new home, so neither of them feels they have dibs on the place.
The trick is to introduce them slowly and gradually, if they get into a fight and make a bad first impression, may be hard to repair the relationship after that.
Best results the younger they are, getting acclimated to other animals is easier then. Dogs and cats tend to have different body language, play differently, so that can be a problem unless they learn that young.
Check with your vet, they'd probably have better info than a gun forum...