Horned Lizard
Source: Pet Battle. Not only is it quick, it's loud too! Beast type. According to the Pet Journal, these are captureable in the Badlands and Silithus, which does not appear to be true.
The Horned Lizard is a wild battle pet found in Uldum that can be captured at level 23.
Guide awaiting review
Travel to Uldum
Head to Uldum to find Horned Lizards. Note that the Pet Journal lists Badlands and Silithus as locations, but these do not appear to be valid spawn zones.
Find Spawns Near Obelisk of the Sun
Two groups of three lizards with fast respawn rates spawn side by side just south of Obelisk of the Sun in the Cradle of the Ancients. Be aware that if you have completed the Uldum quest line, this area may be fully phased out with no pet spawns present.
Check the Northwest Lake
If you have completed all quests in Uldum, lizards including rares can still be found around the lake in the northwest corner of the zone.
Grind Groups for a Rare
Kill two lizards from a group of three, then wait for them to respawn — the respawns are guaranteed to be capturable but will be different quality than the original. Repeat this process to roll for a rare Horned Lizard.
Tips
The three lizards in a linked group all share the same quality, so finding a group with a rare means all three in that group are rare.
Characters who have not completed the Uldum quest line will find more spawn locations active, particularly in Cradle of the Ancients and Neferset.
Binding Interact with Target to a key lets you start a pet battle faster when lizards are near phased areas.