Hi Emma and welcome to the forum and by sounds of things you will be looking to immigrate and
Department of Immigration and Citizenship is a reasonably straightforward menu driven site for those prepared to read in detail.
As to teaching and childcare, I expect that there will be little problem in you both getting work in either State/Territory Capital or regional cities and even some larger country towns though your husband as a PE teacher may be required to also teach other subjects and if he is experienced that way it will help.
One of my nieces and her husband both trained in PE teaching and the husband at a very young age worked his way up through being a secondary school deputy principal to become a principal whilst niece with kids in tow does some sort of schools consultancy - both being the very active type they are, but being a PE teacher at least in Victoria does not restrict you.
Though your immigration to Australia is handled by federal government, with peoples qualifications assessment done by a national organisation education is a state by state affair but with a positive national assessment it is just a matter of registration with the state authorities be it for public or private schools employment, and employment administration may be handled slightly differently from state to state with some states having empowered school boards for employing, there often being some regional educational office oversight.
Childcare employment is less regulated and though a high demand in that area, it is so at the starting level because of low wages but there can also be opportunities at centre director levels etc.
Obviously employment opportunities can vary with a nations economy at any time but teaching I'd expect to vary less, and I'd spend your time now googling Australia and it's regions to find out what sort of area do you want to live in - drier SA and WA, cooler/cold Tasmania, temperate coastal Victoria or NSW, both drier with hotter summers inland, or going more tropical in Queensland or Darwin way.
