That depends. Memory Beta says there have been three different Brisbanes asserted by various works -- a Miranda-class ship in a couple of RPGs, an "Aerie-class" colony ship in the Armada II video game, and an Excelsior class in the infamously error-laden FASA TNG Officer's Manual. If the book didn't specify which it was, it could be any or none of those.
Yes I checked Memory Beta, and wasnt particularly taken with any of those choices. I wouldnt have minded Excelsior, but not with that pedigree.
Maybe a smaller, mid-size cruiser like Norway or Steamrunner, dont seem to see those classes much in Trek-lit.
DRG, any thoughts?