In order to maintain your status in Canada, you need to comply with the terms of your visa and work permit. In order to get PR through the live-in caregiver program, you need to comply with the bellow:
There are two options for determining whether you meet the employment requirements of the Program; you will be required to select one of the following two options on the Document Checklist (IMM 5282).
Having completed 24 months of authorized full-time employment as a live-in caregiver within four years from the date you entered Canada under the Live-in Caregiver Program, OR
Having completed a total of 3,900 hours (within a minimum of 22 months which may include a maximum of 390 hours of overtime) of authorized full-time employment as a live-in caregiver within four years from the date you entered Canada under the Live-in Caregiver Program.
If registering your marriage in Singapore will threaten your ability to apply for PR in the time-frame you want, maybe you should consider waiting.
However, if there is a time limit on registering your marriage, then you should probably do that as soon as you can.