The Powerhouse Markets at New Farm, are also very doggy friendly! The stalls are even set up near the dog off leash park there!
There is usually some doggy stands as well.

Thanks for the information - I've checked out the markets there before, but it was before I got Eddy so I probably wasn't paying enough attention to the doggy stalls! Eddy also loves the off-leash dog park there, so we'll definitely check it out next time we have the chance :)