I've seen British RN's and other like South Africans as well. Singapore has a shortage of RN's and imports quite a few from the Philippines as well. I would forsee very little problem in obtaining a postion here (is your RN from a 2 or 3 year school of nursing?)
The downside of this is the salary structure. Unfortunately the rates are not conducive to coming to Singapore for that primary purpose. That said, if you are a trailing spouse and don't want to spend you life beside the condo
pool (you obviously have a humanitarian streak or you wouldn't be a nurse), nursing would be a viable option. The median salary for "Professional Nurse" is around S$2500-2600 /month. An Industrial Nurse (private sector) around S$3500 /month. ( S$ 1.63:$1.00 US ).
Hope this info helps.