This could possibly be counted as common sense, but if it is I'm not sure why I'm the only one doing this on my server, and I dare say this could be done easily from level 1, with as little as 1 copper.
To start off, make sure you have Auctioneer installed and set up, then run an alt over to a Neutral AH (I like Everlook, as its nice and quiet). Ideally, make sure you're carrying a good few hundred gold.
The reason I say to use an alt is the people whos pets you take will be really REALLY annoyed at you after this. I've already had 1 death threat from this.
Right click on the button shown below. This'll open up your realtime scan config.
Under Searchers, goto Snatch, and add all of the Argent Tournament pets using the '/snatch <itemlink> <price>' command (eg /snatch [Mechanopeep] 100g). I recommend using 100g as the price amount, but you can set this as high as you like to ensure you catch everything.
If you need the item links, here are all of the pets in wowhead, and by request of Emo_Suace, I've added the commands to get the item link in game.
Alliance pets:
[Ammen Vale Lashling]
/script DEFAULT_CHAT_FRAME:AddMessage("Shift-click this to place a link into a chat message: \124cff0070dd\124Hitem:44984:0:0:0:0:0:0:0:0\124h[Ammen Vale Lashling]\124h\124r");
[Dun Morogh Cub]
/script DEFAULT_CHAT_FRAME:AddMessage("Shift-click this to place a link into a chat message: \124cff0070dd\124Hitem:44970:0:0:0:0:0:0:0:0\124h[Dun Morogh Cub]\124h\124r");
[Mechanopeep]
/script DEFAULT_CHAT_FRAME:AddMessage("Shift-click this to place a link into a chat message: \124cff0070dd\124Hitem:45002:0:0:0:0:0:0:0:0\124h[Mechanopeep]\124h\124r");
[Teldrassil Sproutling]
/script DEFAULT_CHAT_FRAME:AddMessage("Shift-click this to place a link into a chat message: \124cff0070dd\124Hitem:44965:0:0:0:0:0:0:0:0\124h[Teldrassil Sproutling]\124h\124r");
[Elwynn Lamb]
/script DEFAULT_CHAT_FRAME:AddMessage("Shift-click this to place a link into a chat message: \124cff0070dd\124Hitem:44974:0:0:0:0:0:0:0:0\124h[Elwynn Lamb]\124h\124r");
Horde pets:
[Enchanted Broom]
/script DEFAULT_CHAT_FRAME:AddMessage("Shift-click this to place a link into a chat message: \124cff0070dd\124Hitem:44982:0:0:0:0:0:0:0:0\124h[Enchanted Broom]\124h\124r");
[Durotar Scorpion]
/script DEFAULT_CHAT_FRAME:AddMessage("Shift-click this to place a link into a chat message: \124cff0070dd\124Hitem:44973:0:0:0:0:0:0:0:0\124h[Durotar Scorpion]\124h\124r");
[Mulgore Hatchling]
/script DEFAULT_CHAT_FRAME:AddMessage("Shift-click this to place a link into a chat message: \124cff0070dd\124Hitem:44980:0:0:0:0:0:0:0:0\124h[Mulgore Hatchling]\124h\124r");
[Sen'jin Fetish]
/script DEFAULT_CHAT_FRAME:AddMessage("Shift-click this to place a link into a chat message: \124cff0070dd\124Hitem:45606:0:0:0:0:0:0:0:0\124h[Sen'jin Fetish]\124h\124r");
[Tirisfal Batling]
/script DEFAULT_CHAT_FRAME:AddMessage("Shift-click this to place a link into a chat message: \124cff0070dd\124Hitem:44971:0:0:0:0:0:0:0:0\124h[Tirisfal Batling]\124h\124r");
After setting this up, go down in your config to options>realtime, and check 'Snatch' in the checkboxes.
Once all thats set up, just left click on the button shown in the image, and your search has started.
This will now buy ANY argent tournament pet that's listed on the AH for less than 100g. So far tonight, whilst I've been writing this guide, I've bought a Elwynn Lamb for 1c, and a Tirisfal Batling for 15g. These will then both resell to give me a massive 3/4000g profit in about half an hours work. This will work better or worse depending on how many people use the cross faction trading on your server, but there are always people who'll list these things for stupid prices to avoid the Neutral AH fee.
Good luck, and may your AH-Fu be strong.