I am holding a valid Singapore visa, but I have obtained new passport as the old one was full. I would like to travel Singapore in couple of days. Can I do this?
From the embassy website
I have an existing visa, but had just changed my passport. Can I extend my visa?
We do not do extension of visa. However, we can transfer your current visa from your old passport to your new passport. Please send both your original old and new passports (including current Singapore Visa), Form 14A application form, Australian contact details and a self-addressed envelope to the Singapore High Commission.
There is no fee charged for the transfer of visa to your new passport.
I think its not possible in a couple of days. However, you can call Immigration and Checkpoints Authority of Singapore in below URL to see if its allowed.