You won't be able to apply for most Government jobs and there are many companies which specify you must be PR or citizen to apply. But there will be plenty of others you could apply for. I'd just put you have a visa that allows you to live and work in australia on your CV. Discuss what visa you have if you get offered the job because some employers are wary of them if the post is a permenant one as the visa is TR.
I am told by some members on this forum that searching for work as a dependent of a 457 visa holder is quite challenging. I know every situation is different but some of the members who advised me had personal experiences. So as I understand, its not going to be easy however if you have a hot skill or skill in demand , perhaps it will be relatively easier.
I would also like to know if being based in a bigger city like melbourne , sydney etc actually increases the chances of finding work for a dependent on 457 visa holder? Any opinions?