Undercity Rat
Source: Pet Battle. Even the rats of Lordaeron fell to the apothecaries' plague, chewing upon the tainted flesh of the dead. Critter type. If you're like me, you may have had the misfortune of heading to Undercity and finding nothing but maggots and roaches.
The Undercity Rat is a wild battle pet found inside Undercity proper, shared spawns with maggots and roaches, and requires clearing competing critters to force rats to appear.
Guide awaiting review
Reach Undercity
Undercity Rats are found inside Undercity itself, not in the outer Ruins of Lordaeron or the surrounding Tirisfal Glades. If you are Alliance with no Horde character, create a new Undead character, run to Brill along the road, and take the flight path to Undercity — your battle pets and pet battle skill carry over to the new character automatically.
Clear Competing Critters
Undercity Rats share spawns with Maggots and Roaches. Kill the non-rat critter versions of all mobs in the area, and also defeat the capturable Maggot and Roach battle pets you encounter, to free up spawn slots for capturable Undercity Rats to appear.
Capture Your Rat
Once an Undercity Rat appears as a capturable battle pet, engage it immediately. Killing critter versions of Undercity Rats also seems to cause some to respawn as capturable versions, so continue clearing the area until you find one of the quality you want.
Transfer to Main Character
If you captured the rat on a new throwaway Horde character, log into your main pet-battling character and the Undercity Rat will appear in that character's pet journal. You may then delete the temporary character if desired.
Tips
Rats found in the outer Ruins of Lordaeron are ordinary Rat mobs, not the capturable Undercity Rat battle pet — only those found inside Undercity proper count.