Labor's Penny Wong said the bill will provide "limited protection, but the real leadership has to come from the Parliament and the Government".
The Australian Bureau of Statistics is aiming to get the survey forms out to 16 million voters by September 25.
The form asks, "Should the law be changed to allow same-sex couples to marry?", followed by yes and no boxes to be marked.
Labor leader Bill Shorten urged voters not to delay returning their forms. "It takes 30 seconds," he said.
Prime Minister Malcolm Turnbull has said he will campaign for a yes vote in the non-binding survey but which will likely lead to a vote in Parliament if it gains enough support.
The ABS will close receipt of forms on November 7 and announce the result on November 15.
The bureau is encouraging forms to be sent in by October 27.