You're right, I *would* love to see them together.  When I was a teenager I
had a Lab/GSD mix bitch ( Pollyanna, one of my most beloved dogs ever.)  She
formed a friendship with a white longhair cat that lived a few doors away.
The cat used to come into our garden, and would rub round Polly's chest and
front legs, and Poll just loved it, so much that she would ask quite
frequently to go into the garden to wait for her friend.  When the friend
didn't come after about 15 minutes, Polly would come back into the house
looking sad.
After Polly went to RB, I got whippets.  Most whippets (but not all) are not
very safe with cats. I caught mine once in the garden grabbing a tabby cat
from both ends.  Fortunately, I managed to get it away from them almost
immediately.  It ran off, and recovered, I know that because it belonged to
a neighbour and I went round and put my hands up to it and offered to pay
any vet treatment.
All my dogs have gone to RB now.  Kitty never would have presented herself
at the door on my birthday if they hadn't, she had a few narrow escapes from
the whips herself.
It took several months before she really believed they weren't there any
more.

Tweed