You can apply for a work permit for her but she has to be out of Singapore while it's being processed eg across the causeway in JB if she doesn't want to go home first. Then just follow all the MOM instructions. She'll need to do the maid test if she hasn't worked here before. So will you, if she's your first FDW. She can come back when you get the approval letter and then process the rest of the paperwork and pick up her WP. Our maid's sister did exactly what you want to do and it was no problem.
Please can you tell me how long the visa takes to process while the helper is out of the country
How long will would she need to sat in JB?
many thanks