Best strategy to find job in Aus?

Hi there,

I am a German physio and currently hold my registration in NSW (I cleared the Aecop exams this year). Currently, I am on a working holiday in NZ where I worked in Wellington (in a private practice) and now at Dunedin hospital.
At some point next year, I would like to return to Australia and look for a permanent job (never have worked in Australia since I gained my registration as I came straight to NZ). I know that there are plenty of jobs for physios there but I was wondering what the best strategy would be as I am looking for a employer who is willing to sponsor me with a work visa.
I am a bit undecided whether to look on my own and contact the hospitals/private practices personally or if I should use a recruitment agency as they probably know which employer would be ready to employ somebody who doesn´t have a work permit in Australia yet.
I would greatly appreciate your opinion about this matter! Thanks!

Melanie