Nope, there are no well paying zoos in general, keeping is not a highly paid job, but those others with chimps aren't going to be any better than Taronga pay wise. Are you near Perth Zoo? If so ask them about vollie opportunities. I have to also point out that even following what I suggested won't guarantee you a position with chimps. Ape keepers tend to try to keep their positions, so they won't come up very often.
You also have to realise that keepers spent 90% of their time cleaning, so basically that is what you will be doing, it won't be a job playing with chimps, and some won't be interested in you anyway.
Vollie opportunities = volunteer positions. I wouldn't want to be a keeper for anything, hence my long stint at uni.
There are only one or two zoos where you can work with chimps in Australia -Taronga (which you don't want) and Rockhampton Zoo (unlikely). So your options are very very limited.
Monarto Zoo is building a chimp facility, but they will be wanting experienced keepers, as will any zoo. You need to do lots of hard yards first, become experienced, known, and respected, and then wait for a position to come up.
And as I said, there's a long, long line of people ahead of you.
Taronga zoo looks like a nice place to work but the houses around there cost between $500,000- $600,000.