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] Azshara; [3-6] Silverpine Forest; [3-6] Loch Modan; [3-6] Darkshore; [4-6] Ashenvale; [5-7] Duskwood; [6-7] Wetlands; [6-7] Hillsbrad Foothills; [10-11] Western Plaguelands; [11-12] Feralas; [12-13] Dustwallow Marsh; [15-16] Moonglade; [18-19] Terokkar Forest; [18-19] Nagrand (Outland); [18-20] Blade's Edge Mountains; [20-22] Howling Fjord; [21-22] Sholazar Basin; [22-23] Crystalsong Forest; [22-24] Mount Hyjal; [23-24] Twilight Highlands; [23-24] Tol Barad Peninsula;  Nagrand (Draenor)
Grooms face and sniffs air.
Pit-pattering footsteps; vocalizations (on-click)
100% Hit Chance
Scratches the enemy, dealing 394 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 3 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.
Critters are immune to stun, root, and sleep effects.
50% from Beast abilities
33% from Elemental abilities
I found the rare as a secondary to Mouse in the Wetlands.
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.
I'm guessing "Uncommon" is the best quality you can get for the Squirrel?
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.