what's your housing budget?
will they also pay DEWA (electric and water, if you want gas cooker then you'll use a bottle) there's also a 5% of your rent, housing fee (one of the many hidden taxes out here) will the company pay that?
if you're paying your own DEWA bear in mind that it is much, much more in a villa compared to an apartment. think 200dhs a month in an apartment and 10x that in a villa as a ballpark.
the website expatwoman is a good place to get info but it's down for maintenance prob till Sunday! but do post on there as soon as you can so you'll get lots of answers from different people already living here.
there's a website called Dubizzle where you can search for rentals, you won't find many photos of places but it'll give you an idea of prices.
there are apartment buildings in DIFC, I don't know about schools as DD is only 8 months but use expatwoman for that, I think schools have broken up now and won't reopen until after Eid (1st/2nd week September)
It would be feasible to live in Springs or DSO and for your DH to drive up Emirates Rd/Sheikh Zayed Rd to DIFC, plenty of people drive these distances for work, remember fuel is cheap here. Public transport... there is the metro and the 2nd line will open in August, there is a station at DIFC.
Will the company pay for shipping? most people do not live in furnished places unless it's v short term, you can pick up 2nd hand housing goods cheaply (see the ads on Dubizzle) but if you're arriving now in the middle of summer do you want to be driving round looking at stuff? if the company are paying for shipping, I would bring everything + the kitchen sink!
make sure the deal includes good full medical insurance for all of you, private hospitals are expensive a trip to the GP/Paed can cost 100gbp. there is a good government hospital for children and you can get a medical card for your DS - I would use this hospital if needed without worry.
post - most people get post delivered to there own or DH work place, no nice posties here to deliver to your home! everything goes to a PO Box and the private ones usually have waiting lists! there is an area called Arabian Ranches where they will soon be trialling home delivery for a hefty price - I wouldn't trust it myself!
before you come, get your marriage and degree certificates attested and get a hundred copies of everything, bring copies of DS vaccination schedule and you may need to get him vaccinated for TB/Hep B for school admission but I may be wrong, get multiple passport photos of all of you done, you wouldn't believe how many passport photos you need.
you and your DS will need to be sponsered by your DH (and he by his company) so check that the co will pay the fees and medical for you and DS (blood test - HIV/Hep B and poss xray for you to exclude TB)
ask away if there's anything else you want to know. there's a book called Dubai Explorer it's useful to have as a reference even after you've made the move.
wow! long post... ask away if there's anything else!!