The only way is for her to try to get a job while she is in Singapore on the tourist visa.. Otherwise she can try online for some jobs interviews..
Yes, the government does not recognize girlfriend and boyfriend as relationship in term of dependency pass. So if eventually she cannot find a job in sg, and you really hope she can be here, and you two love each other.. you can marry her!!

8) Then she will have the rights to stay in singapore because of you. From there, then she has all the time to look for jobs..
My 2cent
Cheers,
take care
