FFR and karabor beach are CROWDED

[Tristful]

Any other lesser known moderately dense places for farming wild pet battles? The beach and the area by the neutral flight point in FFR are packed.

[Shingetsu]

Mh... you might try older places in pandaria.
I really liked farming the critters in "The Ancient Passage" (part of "The Veiled Stairs")
or fighting the aquatic pets in Valley of the Eternal Blossoms.

Alternatively you might stay in FFR/Karabor and try to server hop instead?

[Aurae]

Glad mine aren't all that crowded. Yeah, your best best is to attempt some server hops.

[Zonnetje]

I use Moonlit Shore in SMV. Usually has very little competition, it is a bit of a jaunt from a FP, but well worth it.

[Dakaf]

Four winds is still my favorite spot. You won't get the draenor counts toward the monument, but you'll level the pets really quickly!

[Topaz]

The river near mistfall was also very crowded, had do go up to the shrine near whiptail lake to find pets.

[Endaira]

I just go around frostfire ridge near my garrison, most I ever saw was one other person. Sometimes it pays to be on an alliance haevy server I guess.