A couple of years ago, I would have suggested you look at renting an HDB flat and would have told you to go for the adventure... I guess it depends on the type of lifestyle you lead now...
There is no such thing as "country" here. You can live out of town, but you can't find anything really, really cheap. The cheapest possible accommodation that is going to be suitable for a family will be at least 1.5k a month - and that would be an HDB flat miles from anything (even then it would be a very good price). You would certainly not get a
condo within your budget (many cost more than the entire price of the proposed salary...)
Feeding a family of four will obviously depend on the types of food you eat, but it is still very expensive here. All food is imported.
Day care used to cost me about $500 a month for half days, and that was a local day care (you can get them cheaper, but this can be a case of "get what you pay for...")
Honestly, I wouldn't do it. It is not even a very good offer for a single person these days but it is enough for a family to be completely miserable on.
If you really wanted to come to Singapore, I would suggest your husband look into
International Schools (obviously depends on the subject he teaches). The pay and conditions are much, much better and your family would be a lot happier.
The HR will probably tell you that this is what a local lecturer makes. What they won't tell you is that they won't pay you the equivalent of 20% salary into a retirement fund, as they have to do for local lecturers (and that local lecturers are allowed to use this to pay for their housing). You will not have access to public housing or medical facilities - well, you will, but public hospitals cost the same as private for non-Singaporeans and all our housing has to be obtained on the private (read: far, far more expensive) market. We are not allowed to buy
property without higher salaries and much larger deposits... So it is actually impossible for foreigners to live like locals on local salaries.
Sorry not to give you a more positive message. This is not a good offer and your family would not be happy if you have a semi-decent lifestyle right now.