I doubt you do, as the FAA does not issue pilot licences, nor do they issue instructor ratings. The FAA ratings are instrument, multi-engine, helicopters, gyroplanes, gliders, balloons, airships, and seaplanes. If you had 10,000 hrs given, you would also probably be a DPE and gold seal, they have more privileges than a CFI/CFII.
If you tried to convert a FAA CFI/CFII with 10,000 hrs instructional, CASA would only grant a Grade 3. If you were to convert a NZ A Cat, CASA would grant a Grade 1. There is a equivalence in qualification and experience.
And despite Australia having all this higher qualification and multitude of rules the accident rate is double here in GA. Whats the point? Also FAA rules only have one additional requirement above holding a rating for what you train in and that is for instructor training, where additional experience is required. However they do not care about what type of training you have done.
You can look up the FARs on requirerements for an instructor rating, it's only about one page of reading, including syllabus.