My memory is going today I can recall idea of several stories but not actual searchable names. Ugh. Sorry can't recall character names, story name or authors.
FYI- I liked
Snowbound dogs a lot.
I recently read a sweet story with a dog that gets a couple together. One gal inherits a place with guest cabins, that she went to once as a child, from a man she doesn't know. She is driving in the rain into the town & almost hits the dog. She stops & dog jumps in the car. Later sees a woman on side of road dog gets excited so she stops thinking dog belongs to walking women. Other woman has problem with her truck & emotional issues due to abusive cop father & is trying to say a final goodbye to her mom. Dog helps bring them together a few times when mistrust or circumstance drive a wedge.
There's also a story of shy girl who has a dog & meets up with Gal at dog training -- they see each other a dog park & become friendly and get together for dog play dates. Very sweet evolving story.
Then there is story where lesbian runs a pet store something like fuzzy belly. There is a questioning rollerskating hottie who brings her parent's dog to the pet store. She has bf, but keeps thinking about this shop gal & they run into each other a bunch. Dog has role, but I think dog's personality is not a big thing.
Radclyffe has book,
Shadowland about Kyle exploring SM and meets Dane, who raises dogs & works with friends who shows them. I wouldn't read the story for the dogs in it. I would recommend it as an erotic romance, but not for the faint at heart.
If you like Voyager fiction there are a few stories with dogs in them. GL Dartt has a few in her Just Between series mostly in the ones that have alternate universes as that is where dog come from in story. There's a cute one where their dog escapes & has an adventure saving the ship & destroying Harry Kim's quarters when he chases B'lanna's pet around.
http://www.northco.net/~janeway/fanfic.htm#JBStories Sorry can't pinpoint exact story.
Targs are like dogs and if you believe that there is a great Targ that become Seven's pet in H.W.'s Alternate Choices Alternate Consequences. I think the Targ, Toby, shows up in the 2nd part, but you need to read the first part or you'd be lost.
Kali