Cassisian Angels can be Improved Familiars, are small, have a fire (or cold) breath weapon, and can change shape into a dog.
Fire Mephits can be Improved Familiars, are small, and have a fire breath weapon. Not doglike though. I'm not sure what you mean by 'binding' them.
You could go with a Homunculus with the SLA modification (in this case fire belly or fire breath) though this may still not be quite what you want. Hope I could help. In researching this I've found homunculi to be awesome, little, SLA using monsters. :P
Preferably something roughly dog shaped with a bite attack.
"hell hound puppy"
:^)
Could homebrew a different breed of pseudodragon. One that's evil, reddish and breaths a little spout of fire instead of having a poison sting.
There is the tidepool dragon, which is a tiny dragon with a tiny breath weapon. There are two other options that can "kind of breathe" fire - the pseudosphinx and the xiao have a bite attack and can use burning hands as a spell-like ability a few times per day. How does that sound?
As a backup option, you can get a fire wysp, but it more of a elemental ball with tendril attacks.
I was going to mention the Tidepool Dragon as well, as my Skull and Shackles bard just got one. It's fire breathing is as mentioned tiny, only a 5 foot line in air, or a 10 foot steam cone in water. No demonic pacts necessary, just a few bribes and treats.
Brimorak deamon
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Legacy of Dragons has rules for making a pyrausta a familiar. I think it loses fast healing and the heart of flame ability. Making it a tiny, green, fire-breathing dragon.