Must Love Dogs (and other critters)
There probably were services specifically for pet people at the time but I didn't know about them. If I had, I definitely would have participated.
So, having recently become aware of such things, I'll pass on some links. Click here for a site that features new members' pet photos on the opening page, rather than the humans'.
Click here for a site with an adorable opening-page photo. May you find the critter of your dreams!