Online retailers are also responsible under the law, as the laws apply to all retailers.
In practical terms, if it's an online business with no Australian presence it makes it hard to apply the law. Overseas online companies with an Australian presence, such as Amazon, have been successfully prosecuted [1,2,3]. The ACCC is still working through responsibility for third-party sellers, but it seems to be the case that if it is fulfilled by Amazon then it is responsible.