Hi Vallere, I live a fair way north of Rockhampton, but the cultural experiences would be similar, I think.
Public transport in N Qld (& Rockhampton) is terrible. You will want your own transport. It is possible to find a bike trailer to use, just be prepared for the comments.
Queenland state law requires a car seat, but not to the same standards as the US. You may find it difficult fitting your US carseats into Australian size cars, & you may want to buy Aus standard seats when you get here.
Cost of living: we pay about $100 month in electricity, but limit our use, & don't have airconditioning or a pool. We have gas heated water & stove ($70/month), & the phone/internet costs about $130 month. Houses aren't heated in winter, so that isn't a comcern. Petrol for the car averages $1.30/litre ($5.20/gal). We have one car and spend about $200/month in petrol.
Homeschooling is fine here, and has a long tradition in Queensland, as long as you follow the state education requirements (I don't homeschool, but have never heard of probs from friends who do).
You can grow your own veggies year round in Rockhampton, although in summer you will be limited to tropical varieties.
I hope that helps a bit, even though I don't live in Rockie. Queensland is a very chilled place & after 11 years I cant imagine living anywhere else. I still go to the grocery store in bare feet, especially in summer when it's so hot you can't even think straight, much less consider shoes.