Express post has no guarantee at the moment. I would definitely not offer it as an option.

One has to wonder why the customer suddenly needed it exactly today at the latest if they had not communicated this earlier. 

Do not refund her. The item is still on its way. 

Also, sending a replacement order is not a viable way to settle an issue - you would not be covered if anything happened to the second shipment and the customer would ultimately end up with double what they ordered. This option is only viable if the parcel becomes lost as you can then make a claim against Aus Post so that you are also not out of pocket.

At this point, is she asking for a refund, or has she actually opened a dispute? Are you looking on the Aus Post website at the tracking, or just on Ebay? They often show different things.