For a pair of rabbits there is:
一对兔 yī duì tù
And for a pair of shoes there is:
一双鞋 yī shuāng xié
And for twins there is:
How can I be sure when to use 对 and when to use 双?
From "Chinese: A Comprehensive Grammar" (Routledge):
一对夫妇 "a married couple"
一对枕头 "a pair of pillows"
一对耳环 "a pair of ear-rings"
一双手 "a pair of hands"
一双眼睛 "a pair of eyes"
两双鞋 "two pairs of shoes"
三双袜子 "three pairs of socks"
The difference between 对 and 双 seems to be that the former emphasizes complementarity while the latter indicates functioning together.
(Anecdotally, it's been my experience that, due to influence from Cantonese, 对 is much more common in the south even when 双 would be "correct.")
maybe this'll help choose which to use: (i don't know how universal the rule below will work but it works for the examples in this page so far. my logic is to look for the singular of the pair when just the pair is confusing)