Should have thought that it would be next to impossible and if you did it at all, that you would be quite miserable.
Transport is the biggest problem. Unless you can safely (!!!) walk where you want to, a car is amost an absolute necessity in South Africa.
Total budget is R5,600 per month. You propose to spend R2,600 per month on rent, exclusive of utilities? That's 46.5% of your total budget allowance allocated for rent. That's much too high a percentage. Budget a mximum of 33.3% of your total monthly expenditure for rent, in this case R1,860. You probably will not find a little garden cottage for that little amount of money.
Work in South Africa will, in reality, probably not be a problem except that you might not be treated exactly fairly if the employer knows that you are an illegal. If your girlfriend is caught working illegally, the authorities may well deport her and you as well?
That's all pretty negative. It's not meant to be anything other that realistic. Doesn't the EL school have single accomodation you can use in the beginning?
Perhaps your girlfriend could organize a job teaching Spanish in SA before you leave? Possibly a temporary work permit could be arranged that way? Perhaps a cultural exchange might help her find a footing in South Africa although she might not be with you in EL in the beginning.
Have no idea of the cost of living in El Chile although have been looking quite carefully at Argentina recently. Should have thought that Argentina and South Africa were actually quite similar but could be off target in that assessment. In any event, don't think that your budget is quite sufficient and think too, that it is unbalanced.
Getting around really is going to be a very big problem for you if you have no easy access to safe and sensible public transport. Minicabs, for foreigners, female and of fairer complexion than that generally found locally, would not usually be an ideal form of transport.
Being a great believer in the unconventional and always being prepared to seek advice, I would write to the air attache at this site,
http://www.embchile.co.za/embassy.htm
and ask him for any advice and information he might be able to give you. You will probably need to be very, very polite. Pretend that he is Bachelet Jeria!
Suerte hombre!!
