https://community.theasianparent.com/q/i-found-out-im-pregnant-how-i-go-about-i-go-polyclinic-get-referral-l/5106495?d=mobile&ct=q&share=true You can either get a referral letter to go to public hospitals, or if you choose to go private, you can directly call them and make an appointment. You can already do a scan at 6W/7W. Heartbeat depends on whether it can be detected, differs for each person.
If you want it fast, can go to any private gynae. If you prefer SGH, can get referral letter and at the same time can book an appointment via HealthHub App. They will get back to you via 3 working days through email/sms. I would recommend Dr Yang Li Ying from SGH. ☺️