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Obviously there is some confusion here regarding two wars fought at separate times in the same part of the world. The attack on the USN frigate occurred in 1987 during the Iran-Iraq War.
In the Gulf War to which the question pertains, Australia sent about 1800 defensive troops to protect Suadi Arabia during Operation Desert Shield. As they did not participate in the offensive phase, Operation Desert Storm, casualties may be presumed to be light if any. However, many Australians have died in both World Wars, the Boer War, Korea, Malaysia, and Vietnam. The Battle of Khafji was the only battle during Desert Shield, and it occurred in the sector defended by the Saudis and Qataris. Had the Australian sector been attacked, they would certainly have done their part and taken their casualties.