A few of us in my mum group have had good experiences with Dr Hazel Quek at KKH, her consultation is around $150 per visit, which is quite reasonable for private, and the feedback has generally been positive. Dr Manisha is another name that came up, and she's known to be caring even though her schedule can get quite packed, so appointments may take a while. One of my mum friends also mentioned Dr Kannika Chaudhuri as a well-regarded female doctor if you're looking for an Indian lady gynae specifically. Switching after your first trimester is actually a smart move since you'd have already done most of the subsidised scans and tests by then, so you save quite a bit that way!