to Give you a straight answer The money they are offering more than likly wont be enough if you wish to bring your family here as well. taking in to consideration that you have to pay for your acomodation, childs schooling ( around 7000 - 8000 riyals per term depending on childs age and school) as well as youll be expected to more than likly pay for your water and electricity bills, phone ect and depending on what you are used to as far as fresh food is concerned (good quality fruit and vege and meat is quite expensive to give you and idea we are a family of 4 and it costs us around 3000 riyals a month for shopping) your best bet is to see if they would consider a package in the vicinity of 20000-30000riyals a month take home and provide accom and schooling for your child. As far as places for your child in school being a government department they should be able to find them a place but again depending on how old just bear in mind most schools run with the british cirriculum here and they start children in a formilized schooling at the age of 3-3.5y.o so depending on your childs ability he may be droped back a grade this does not always happen but most of the good schools here will require for him to have an assment for this purpose. On the matter of sending money home just be aware with the greenback sliding into decay and the Riyal tied to this sending money home to places like OZ and NZ is becoming increasinly hard ( we just sent 2000 riyals home by the time it got there with the exchange rate it cleared at only $589 AUD) hope this helps with your decision
cheers and good luck