"By convention the prime minister comes from the lower house but I believe this is convention only.......he / she can come from the Senate."
I don't think you understand the reality of politics in this country. Convention or no convention, no party will EVER try to have its leader and prime minister governing the country sitting in the Senate. It just will NOT happen. You don't have to believe me, just be patient, you will never have the chance to see that happens.
The closest it ever came to was when Liberal Senator John Gorton was made leader of the governing parliamentary Liberal Party and hence became the country's prime minister. He subsequently resigned from the Senate and contested the seat of Higgins and won it in a by-election and entered the House of Representatives. I had already posted about this in another thread some days ago.