Hi Patty,
Dogs are often a bigger problem with pet birds than cats are. Cats are more interested if the bird is really active and moves around the cage quickly. Dogs are more likely to knock a cage over to get a bird, or grab a bird when it is out of the cage. The bird certainly isn’t safe where it is. While there were no visible wounds, the bird could have internal damage. You do need to supervise the cat when you bring the bird home, to judge his interest level. And it is best not to leave them in the same room alone, even if the bird is in the cage. Of course never have the cat in the room while the bird is out of the cage. But plenty of people have cats and pet birds and as long as you are careful, it should be fine.
Thank you for asking Lafeber,
Brenda