Can a post-doc with spouse and baby make do without DP?

Hello,
I am an American who has been offered a 2-year post-doc at NUS, but the salary is only $5,500 - meaning I am not eligible for a dependant pass for my spouse and family. I would be moving to Singapore with my American wife and a newborn baby. The chance of my wife securing a job that would give a DP is of course unpredictable. Therefore, assuming she is unable to find work, what other options are available to us? Is it possible to live on a tourist visa in Singapore and make visa runs to Malaysia? Or does Singaporean/Malaysian Immigration crack down on this?

Any advice is appreciated.

Less than $6k, you can't bring your spouse and child. But, your wife can come as a visitor with child (max 2 months both can stay after extended one month, but 3 months is unlikely as they ask specific reason e.g. like medical treatment or exams etc.). If she can't find a job during that time then she has to return. But she may re-visit again and continue to try her luck to find a job.

No way it's allowed you or family to stay in Malaysia then work in Singapore.
Few months back, I have provided detailed information on this in visa category and work category, you may look into my past message to know why it's highly unlike for you to stay in Malaysia & work in Singapore as a foreigner. Good luck

Visa runs are a NO-NO in Singapore. Do NOT attempt that!
There is no realistic chance (and no loophole) for your wife and child to stay in Singapore for a longer period unless they have a proper long-term residence visa like DP, EP, LTVP, etc.