Local to me are DRB & Harrison manufacturers. I can highly recommend both. I have built both a DRB & Harrison Cobra. Both Peter Ransome(DRB) & Warrick Harrison(Harrison) are enthusiasts and active club members.
Both can supply all the parts required to complete the car.
Both currently ship cars overseas in various states of completion. So both would be experienced enough to handle your overseas order.
Not sure of any other Australian Cobra manufacturer that ships cars overseas.
DRB web site is above.
Harrison web site
www.cobrakits.com.au.