The answer is:
Animals of the Chinese Zodiac, in order starting from Rat
By line:
A dirty creature who walks on all fours.
RAT; direct clue
Queen zebra
OX; first letters are QZ, which is OX rot-2ed
White Light just had unbind
TIGER; first letters are WLJHU, which is TIGER rot-3ed
Very enthusiastic four fowls make X
RABBIT; first letters are VEFFMX, which is RABBIT rot-4ed
9 63 6 2 60 69
DRAGON; these numbers are the A1Z26 encoding of 'DRAGON', with each digit rot-5ed over the digits 0-9 (D=4 -> 9, R=18 -> 63, A=1 -> 6, etc.)
Young to go quirky kicks
SNAKE; first letters are YTGQK, which is SNAKE rot-6ed
Orange violet yellow zeal lime
HORSE; first letters are OVYZL, which is HORSE rot-7ed
Apple pineapple mango mangosteen xigua
SHEEP; first letters are APMMX, which is SHEEP rot-8ed
Vulture xylophone width thing net hot
MONKEY; first letters are VXWTNH, which is MONKEY rot-9ed
Blob yell yall chocolate doe over black
ROOSTER; first letters are BYYCDOB, which is ROOSTER rot-10ed
Over zealous rage
DOG; first letters are OZR, which is DOG rot-11ed
Crouch very tight
PIG; first letters are CVT, which is PIG rot-13ed (note rot-12 is skipped)