Is it worthwhile trying to get my bub used to her travel cot before we leave Singapore or is it best to just go cold turkey and see what happens?

I would say depends on your baby's adaptability. My baby has inherited my nature of being able to sleep almost anywhere and anytime. Haha. She sleeps when she wants to, no matter where she is. If your baby is sensitive to changes then you probably should get her used to the cot before flying off.