Can the appropriate MP's choose their ministerial position? Or is it delegated to them?
Thanks for your question Jessica.
The Prime Minister decides which members of the government become ministers. The Prime Minister chooses experienced and knowledgeable government members to be ministers and expects them to work together on behalf of the government. Although members of the government team may have views about who should become ministers, it is the Prime Minister who decides.
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.