Well it depends on a few things.
Are you, personally paying for the shipping? If not, bring your things. However,
Will you be staying a place large enough to store the items when you no longer need them ?(it seems like that day will never come but believe it sneaks up on you very quickly)
If you bring your crib, etc... will you be willing to selll it here once your son outgrows it? Does it have sentimental value?
Just bear in mind mattress sizes vary between Asia, US, Europe, Australia, so mattresses and bedding could be a problem. Also, like everywhere, there is a huge range of prices for cribs, etc. The changing table at IKEA is S$40, definitely not of 'family heirloom' quality, but will get you through the next 12 months I would think.
You could try to rent a crib and buy your own mattress. I had three cribs in use at my house for a while: we had new, used and rented. It all works out...
Good luck with your move,
P.S. Reminds me, when we moved to Singapore 11+ years ago, a used US-made crib was the first thing we bought. I wheeled it from the Colonade apartmnets where I bought it up to my Four Seasons Apartment. Can you imagine? It was the only peice of furniture we had for about a week.