Dear Nelly
There are really three ways that most expats go:
Mt Elizabeth Hospital with Dr Ann Hagerty or Dr Yeoh;
Gleneagles with Dr Shirin Jacobs; or
Thompson Medical Centre with Dr TC Chang or Paul Tseng.
Mt E is the most glamorous and similar to a private Australian or English Hospital. It is a general hospital with a large maternity ward.
Thompson has the best reputation for nursing staff, excellent lactation and parent craft teachers and is a specialist Maternity & pediatric hospital.
Gleneagles gets mixed reviews and the last three people I know who delivered there checked out early.
6-7 Months is not too late to book in to a hospital here (though you'd be stuffed if you tried that in Australia) so you should be ok.
You'll probably want to meet a couple of the Dr's once you arrive, and then choose your hospital based on where they deliver.
Good luck.