Shouldn't be too hard to do, depends on where you are coming from and what they are used to,and of course how old and set in their ways they are (ie. climate and environment..garden, house, flat etc) It also depends on where you are going to live whether they will take animals, particularly dogs, but small dogs are normally fine, as are cats. Check it out with your housing agent if you have one already.
If you have a cat I would recommend that you bring it if is used to being indoors all the time. I would not recommend Singapore as a place to have a cat that is used to wandering around outside. In most cases there are not many places to wander, and secondly lots of people here don't like wandering cats and tend to report them as strays.
Having said that please don' t let me put you off. We have two cats here that we got from the Cat Welfare Society and they love it here, they are now both indoor cats, something I would never dreamt of having before coming to Singapore. They love it.
Good luck with your move.
PS the recommendation from previous poster about petmovers is good...they seem to be really good and helpful too.