After reading Spiritoflove's comment, I also decided to try farming with a different race.
I farmed this pet for about an hour on my level 90 human priest. I found only greys and whites during that time. Next I tried farming on a newly-created level 1 blood elf mage. I found a rare on my 5th battle. In total, there were 2 whites, 2 greens, and 1 blue while farming with the level 1 blood elf.
Taking a brand new blood elf certainly worked. Whether it's a matter of race or level, I cannot say.
1843 pets
After reading Spiritoflove's comment, I also decided to try farming with a different race.
I farmed this pet for about an hour on my level 90 human priest. I found only greys and whites during that time. Next I tried farming on a newly-created level 1 blood elf mage. I found a rare on my 5th battle. In total, there were 2 whites, 2 greens, and 1 blue while farming with the level 1 blood elf.
Taking a brand new blood elf certainly worked. Whether it's a matter of race or level, I cannot say.