There is a cooking recipe which makes [Critter Bites], which allows you to have any critter you come across become your minion for 3 minutes. While as your minion, they act as any normal non-combat pet, and will follow you around. The best thing is, that you can have as many out as you can.
To obtain this cooking recipe, you must do a few of the Dalaran cooking dailies to obtain [Dalaran Cooking Award]. You can then turn in three of the awards for the [Recipe: Critter Bites]. If you are not a cook, go steal some from your cooking friends, or find them on the Auction House.
You will also get the Critter Gitter Achievement for using the Critter Bites to attract 10 critters in under 3 minutes. The place I found to be a very easy location to obtain this achievement was at the house of the Crazy Cat Lady. Right around the inside and outside her house, she has eight cats running around, as well as two cows in her backyard. Target each critter and use the Critter Bites on them. Next thing you do is ride back into Stormwind to show off your new entourage, and show them Hunters how to really tame pets.
Of course this is only for the Alliance, unless a few of you Hordes out there are filling a little adventurous. Another location I can think of is inside the Tram area that goes between Stormwind and Ironforge. There are many rats running around for you to tame. I’m not too sure where you can go for the Horde side to grab this achievement as easily as the Alliance. If you got a location, let us know!