Working on a Tourist Visa?

Hello all!

I was just hoping for some advice about the Tourist-Working-Visa-Conundrum. I'll be arriving on the 3rd of March with the intention to work as an English teacher. I have not found anything concrete yet but will be back in contact with some people after Tet.
My concern is that I a) cannot work on a Tourist visa (that I am aware of); and b) cannot change from one visa to another once I am there. If I apply for a Tourist visa, the form requires an exit date to be provided, which I don't have. I know of people who crossed the border into neigbouring countries to re-apply for a visa. Is this a similar experience for anyone? What did you guys do in this situation?
I guess the specific visa requirements may be more applicable to other Australians but if anyone has any advice, I would really appreciate it! Thank you! (And sorry for the mini-essay).