Can an LGBTQ person run for Prime Minister?
Thanks for your question. In short, yes, they can!
The Prime Minister is a member of the House of Representatives and leads the parliamentary party, or coalition of parties, with the support of the majority of members in the House. They are chosen as party leader by the members of their party.
A number of LGBTQI people have been elected to Parliament and have been chosen to be parliamentary leaders.
The government side of the House of Representatives

Penny Bradfield/DPS AUSPIC
Description
The leader of the government is the Prime Minister, who stands and speaks at the main table in the House of Representatives. Members of the government sit in the 5 rows behind the Prime Minister. The government is the party or coalition of parties with the support of the majority of members of the House.
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.