This past year, 3 out of the 4 kids in our family lost pets. My brother and SIL lost their dog unexpectedly and my sister and BIL had to put their dog down. We also had to put down our beloved horse, Cody. It was very hard on each family and we all supported each other with cards, calls, email, etc. My brother drew my name for our Christmas exchange and donated money to the humane society in Cody's name. That was one of the most wonderful gifts I've ever received. Obviously, your brother was a dog lover, so I say absolutely - a card would be a very nice gesture. It's not how you felt about the pet, but how they felt about their pet. To know that someone cares enough for them to support their grief, has to be a comforting feeling.
Be honest. Tell them you know you don't have any words to make them feel better, but they should know that you are thinking of them.
*One thing I will never forget is an email I received before any of our family lost their dogs. I wish I could find it again, because I've had to paraphrase, but this is the basics.......a vet was making a visit to a family who were having to euthanize their dog. The vet was talking to the young son about why their dog was having to have this done. The parents were explaining why dogs have a shorter life than humans. The boy seemed to understand completely, so they asked him his thoughts. He said he knew why dog's lives were shorter.....it was because they learned how to love before people did. They learned unconditional love a lot faster, so God says
"You did a great job, you can come home, now." That always sticks with me. This is why dogs rock. :)