Are there any jobs to teach ESL at private academies in Australia?

If you are planning to come over on a WHV but not if you are looking at coming over on a migration work visa. The jobs that are in the private colleges are rather hard to get and since you will only be able to stay there for 6 months, you would not be an attractive potential employee. Secondly the jobs are very part time - 1-2 days a week, not enough to survive on.