Need info for Australian wanting to live in prauge (Prague)

Hi my girlfriend is slovakian currently studying in prauge and I would like to go and live with her for a year or two but Australians cannot get a working visa for either country. Could anyone give me any ideas or suggestions on how I could come to stay. I'm going to be doing a TEFL (teach English as a foreign langauge) course, but still unsure if this will help.
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Thankyou for your help