Can I use the same name as another product?

As it is often the case, the answer to your question is, "maybe". Assuming your mark is identical to the Australian mark even though for similar goods, you may be able to obtain a trademark registration in the US for the mark. As a general rule trademark rights are limited geographically. That is to say that an Australian trademark registration will not in and of itself be enforceable in the US. The obstacles you may run into are that if the Australian's have sold their product with the mark in the US, they may have common-law rights that precede you. If so, the Australian's have the right to challenge your trademark application in an Opposition proceeding, or if after you register, in a Cancellation proceeding. As you may know, trademark rights arise from earliest continuous use of the mark. The Australian's are the senior user under these facts.Additionally, there may be other users of similar marks that you are not aware of. Finally, it is important to know the strength of your candidate trademark. If it is generic or merely descriptive, it cannot be registered or enforced as a trademark. Whereas, if the candidate mark is fanciful or arbitrary it is a strong mark that can be registered and enforced. Accordingly, you should seek the advice of trademark counsel based on a complete understanding of your facts, namely the marks and goods associated with them, and have a trademark availability search performed to better advise you on whether to pursue that mark at all. It may be the case that you should select some other mark to avoid legal problems down the road with your candidate mark. It can be costly to unwind an advertising campaign based on a mark that infringes another's mark.

If they do no have sales or a meaningful brand presence in the US, then they would not bar you from using that name in the US.