It is indeed rhyming slang, originally from the East End of London, but taken to Australia by English emigrants. The source is the phrase cobbler’s awl.
An awl is an ancient pointed tool for making holes in things, the most characteristic tool of any leatherworker; it was an essential part of the shoemaker’s kit, since he was forever piercing leather to sew pieces together. So a cobbler’s awl was as characteristic of his trade as his last, or foot-shaped anvil.
The rhyming slang linked cobbler’s awls with balls, that is, testicles. As was usual with such rhyming slang phrases, the first word later appeared on its own as a kind of half-disguised code, so cobblers! came to be used in the same way as balls!, as an exclamation of derision or disbelief, suggesting something was rubbish or nonsense. The examples in the big Oxford English Dictionary suggest that this last sense is actually quite recent, only being recorded in print from the 1950s onwards (though very probably older in the spoken language).
A load of old cobblers is an intensification of that, once commonly heard in London as well as in Australia and also in other Commonwealth countries. Americans seem never to have got into the habit of using cobblers! (or indeed balls!), though British cop shows exported to North America have made both retorts familiar to many there.