Queen
The Queen's Throne/Chair resides in the Senate chambers. All the seats and the carpet in the Senate chambers are colored red. The reason for this is because royalty only walks on red carpets. As I wrote, the Senate is the Upper House/the more regal house and was based off of the tradition of having a legislative body consisting of "Lords". The Queen/Crown would refuse to discuss issues with the "commoners" and would only talk with the "Lords" on a red carpet. English law has a very strong influence in Australia (note the Crown, Lion and Unicorn) and thus Australia adopted many English traditions. Also, it is punishable by jail and by fine to sit in the Queen's chair.