
Two suggestions........find your local amateur photography club (library will have info) & ask if one of the members will "have a go". The standard is usually as high as a pro at these clubs so don't be put off. They will charge very little but want to use the pic in a portfolio/exhibition if its any good.
option 2.........Kodak run a pet portrait award monthly, which most professional portrait photographers enter. A lot of them will do the sitting for free & only charge you if you decide to buy something off the proofs. Ring around a few & see. Your dog might even win the competition!