I totally get the nerves for your first time, it's so normal to feel unsure about where to deliver. Honestly, I'd say the most important thing is finding a doctor you feel comfortable talking to and asking questions, rather than chasing a "famous" name, especially since you're already in third trimester and need continuity of care. If you do want to switch to private at KKH, just call their private clinic directly and they can match you with available doctors and let you know about transfer processes. But if you stay with the government scheme, KKH doctors are really experienced and the system is solid too, so either way you're in good hands lah. Maybe do a quick chat with your current PD or OB to see what they think would work best for your situation?