Pet Battle:  Gilneas;  Stormwind City; [1-2] Azuremyst Isle; [1-2] Elwynn Forest; [1-2] Dun Morogh; [1-2] Teldrassil; [3-4] Westfall; [3-6] Loch Modan; [3-6] Darkshore; [3-6] Azshara; [3-6] Silverpine Forest; [4-6] Ashenvale; [5-7] Duskwood; [6-7] Hillsbrad Foothills; [6-7] Wetlands; [10-11] Western Plaguelands; [11-12] Feralas; [12-13] Dustwallow Marsh; [15-16] Moonglade; [18-19] Terokkar Forest; [18-19] Nagrand; [18-20] Blade's Edge Mountains; [20-22] Howling Fjord; [21-22] Sholazar Basin; [22-23] Mount Hyjal; [22-23] Crystalsong Forest; [23-24] Tol Barad Peninsula; [23-24] Twilight Highlands
Grooms face and sniffs air.
Pit-pattering footsteps; vocalizations (on-click)
95% Hit Chance
Scratches the enemy, dealing 433 Critter damage.
100% Hit Chance
Instantly deals 236 Beast damage and causes the target to Bleed for 98 additional Beast damage per round for 4 rounds.
Deals 197 Critter damage and increases your speed by 75% for 3 rounds.
The user lowers its body close to the ground, reducing all damage taken by 50% for 2 rounds.
80% Hit Chance
Hurls nuts at the enemy, dealing 531 Critter damage.
Nuts continue to fall on the enemy's current pet dealing 59 Critter damage each round for 4 rounds
Starts a stampede, causing 177 Critter damage.
Opponents struck by the stampede take double damage for 2 rounds.
Stampede continues for 3 rounds.
I found a surprising number of Rares in the Crystalsong Forest -- possibly because they're nearly tripping the Blue Dragonkin wandering around waiting to kill you. The more dangerous the location, the more likely the Rare, it seems.
First time I saw one, I got a rare!
I'm guessing "Uncommon" is the best quality you can get for the Squirrel?
Squirrel also spawns in Sholazar Basin level 21. I have seen 2 spawn there as main battle pets.
Although it's not listed:
you can find Squirrels in Westfall. I stumbled upon one next to Sentinel Hill.
It was rare and it was level 3.