If the opposition won the majority in the Senate, would they sit on the right of the President?
Thanks for your question.
As you know, at a federal election the party or coalition of parties with the support of the majority of members elected to the House of Representatives becomes the Australian Government. That team will sit to the right of the Speaker of the House of Representatives and to the right of the President of the Senate. So even if the opposition had a majority in the Senate they would still sit to the left of the President because they wouldn't be the government.
Layout of the Senate

DPS AUSPIC/Parliamentary Education Office (peo.gov.au)
Description
Position of where the government, opposition, minor parties and independents sit in the Senate:
- The government sit in the seats to the right of the President of the Senate's chair.
- The opposition sit on the left side of the President's chair.
- The minor parties and independents sit in the curved seats at the end of the 'U' shaped seating in the middle.
Permission should be sought from DPS AUSPIC for third-party or commercial uses of this image. To contact DPS AUSPIC email: auspic@aph.gov.au or phone: 02 6277 3342.