Hello Lindsey,
That depends entirely on the kind of qualifications you have (or don't have). What you may have heard is that you need to first go through a skills assessment. This is actually the first part of the permanent visa process.
It does not involve re-training, but it does involve having to prove that you are an electrician. (Not a difficult thing to do if you are an electrician, although it's a bit trickier if you are trying to get to Australia by pretending that you are an electrician

)
At the end of that process you get a provisional licence which allows you to work in Australia. But some Australian states do then need you to take a short course to get up to speed with Australian electrical health and safety requirements. That's only logical.
If you do not want to go to Australia permanently then the process is even simpler: there is no need for a skills assessment, but you do have to apply for minimal licensing once you get out to Australia. Again, the type of license you have to apply for depends on the part of Australia you will be going to.
Australia is divided into States and Territories and each is governed by it's own laws, as well as being governed by one set of Federal laws. It is an annoying system, but that's the way it is.
Cheers
