by corolla, you're referring to ae86 corolla fr's yeah?
most parts will fit the aus spec ae86, so if you're into importing trueno bumpers and bits, you can rest assured that they will fit. (they're all ae86s and the chassis' are pretty much the same - in fact your ae86 will have drilled holes in it ready for a trueno facelift!)
if you're thinking of getting rear axles (i.e., to fit that long awaited LSD), you'll have to either find zenki ones (83-84) or modify your car to fit the kouki ones (85-87). kouki ones are stronger btw.
you ought to check out club4ag's technical section to check out the technical differences between the various ae86s out there.
i've personally bought a few auto bits and pieces from ebay... IMHO, its one of the best ways to do it cos its quite hard to find australian distributors for certain parts you're after. ae86 racing isn't too big here, so we have a short supply (if any at all) of performance parts for em.
i've find that its relatively safe to trade on ebay. be prepared for long waits though.. and they often do charge a fair bit extra for shipping to here (depending on weight, size etc).