Understanding DETC accreditations.

Hi everyone.

I signed up to make this post and have read through a couple topics and I hope someone would be able to help me out.

I attended a public highschool in Nevada in 2005, passed all my classes, but failed the newly introduced High School Proficiency exam. I am since traveling and I'm looking at applying for an Australian Working Holiday Visa, which has a requirement of "High school education or equivalent".

I have been researching two possible DETC schools, specifically Allied national (Online High School Program for Homeschooling - Allied High School) as I only need to complete the maths credit.

My question is, are DETC accredited institutions recognized as equivalent education providers? I've been doing a lot of reading and there is a lot of rhetoric surrounding the issue. My concern is that if I gain a high school diploma issued by a DETC accredited school, will it be recognized by the Australian government?

Thanks for any information!