If you live in a nice 2 bedroom apartment starts around $3000, maid and levy $750, utility bills $500, food etc depends on you , also phone , car or taxi fare etc. ....... It all adds up, i am not trying to scare you or put you off, but try and get accomodation allowance if possible.
Like I said elsewhere, rents start at $1500. HDB Flats are good enough for approximately 90% of the Singaporean population. There is no reason why you need to pay condo
prices unless you just want bragging rights. As you did not indicate if your wife is going to be working, I will assume not (at least at this point). Therefore there is no need to hire a maid (again, unless you are looking to Singapore for bragging rights or to make money). Cars are unneccessary here (I've done without after selling mine in 1988 and using public transport ever since. (and raised two kids from infants as well.
Additionally, depending on your lifestyle, if you are a heavy drinker (which I tend to doubt) it will cost you. Food is cheap here (especially indian food) and most anything else can be gotten here to make you feel almost at home.
For your information, the average Singaporean "median Household Income" is around $4500/mo (that household - with usually 2 working and not individual income). Most of the "expats" here like to inflate the numbers. Why I'm not sure, maybe to scare of the competition. Who knows. But, Yes you can save money here. I would say easily 2500/mo without trying and more it your purpose here is to earn & build a nestegg. The only thing that could through a spanner in the works would be the education of your child. You did not indicate the child's age. If pre-school you will be okay for a while. Odds are you will eventually sooner or later (probably sooner) apply for PR. If so, you will probably put them in the local school system (smart idea actually). This will also keep the costs down.
Okay, that's a wee bit more detail than my first "yes and yes".