You can arrange a transfer yourself online for free without going through an agency. If you do want to have someone take care of the transfer I know someone who will submit paperwork for you for around $150 much cheaper than agent.
Please bear in mind agencies will also charge the maid at least one months salary so they make quite a bit of profit for something that can be done for free.
Here are details:
Apply for a new work permit for a transfer foreign domestic helper:
Preconditions:
The current work permit is still valid 30 days or longer.
The current employer stays still 30 days or longer in Singapore.
the current empl. gives a letter of consent (release letter) by either completing Part 5 of the Work Permit Application Form or by writing a letter.
The domestic workers passport is valid for another 7 months or more.
Application procedure:
Get a Singpass:
http://www.singpass.gov.sg/sppubsvc/req1.html
Take the Employer Orientation Program (EOP) online course:
http://cec.sp.edu.sg/webapps/login/ The course will take about 2 hours to complete. You will need to print a copy of the Certificate of the Employer Orientation Program (EOP).
You can now apply for the Foreign Domestic Worker’s Work Permit online here. You can pay the S$10 administration fee online using your credit card. Please check this site again the following day for the status of your application (i.e. Received, Pending). When you see the status as “Pending”