Hi Burnsey - I'm also an Aussie and have been here since February.
1. Yes, you need a good compound - try and get your full accom costs as part of the package - as all the western compounds are very expensive; you will need at least SR80 000 on most for a 3bd townhouse, sometimes up to SR120 000. Almost all of the main compounds have the facilities you mention (pool/gym etc) and generally the people are a mix. There are people with young children on all the compounds. Try googling "Destination Jeddah" - they list the compounds here and if you can find their article from the April 2012 issue it gives details about 10 of the main compounds here in Jeddah. They don't talk about Saudi City - which is the largest compound in Jeddah, but also the oldest - but if you want some info about it send me a pm.
2. Schools - there are no schools in Jeddah that teach the Australian curriculum. The two schools I would suggest are Jeddah Prep & Grammar (The British-Dutch School) or The British School (The Continental School or Conti). They both teach the British curriculum which is close to Australia (a bit higher/more rigorous actually). Our schooling system, including the new Aust curriculum, is closely mapped to the British curriculum.
School year is Sept-June so depending upon when you arrive as to how easy it may be for your daughter to get a place. When we arrived there was no space for my youngest in the nursery classes of the 2 schools I suggest, but he did get a place in a small preschool on our compound, which was very convenient. At age 4, kids are in "nursery" and move into "reception" at around 5. My younger son is 5 later in the year and will start reception in Sept of this year. Both of these year groups only attend school for half a day - finishing at lunchtime (about 12.30).
Fees are substantial - you will need at least SR35 000 per year for school fees PER CHILD, you need your contract to specify that they will pay the FULL amount of any school fees. This doesn't include uniforms, books etc - you can try to get a deal for school 'expenses' which allows you to claim these things if the company will agree, but really they are not very expensive - we paid about SR500 for uniforms for our older son. The fees at Prep for Reception are SR33 000 for the year, and SR35 500 for Yr 1-5; there is also an additional SR7000 in initial enrolment fees. Conti's fees are similar.
3. Depending on the company - wrt flights - it is highly unlikely that you will get more than 1 flight per year, and many will not pay at business class level. Sometimes they will pay business class for your husband, but not for you - depends on the company. I wouldn't bother trying to negotiate extra fares - I haven't heard of any company that does this.
Flights within the middle east are relatively inexpensive - its rather like buying fares from Brisbane to Sydney or Melbourne - about the same sorts of costs. Plus you can get holiday deals via websites etc like at home and the airlines here still have children's fares - so you only pay half price for them. There really is nothing to spend your money on here - except travel! You can have a nice family holiday in Dubai (Abu Dhabi is better!) for a family of 4 for a week for SR5000 - less as you obviously won't pay much for your infant.
Hope this helps - I've sent you a pm also with some other details!
Cheers