Is there a Christological doctrine that teaches that Jesus wasn't originally divine but inherited or became divine, being exalted into divinity by the Father as the result of an act or event?
Did Jesus inherit divinity? ...was Jesus originally without divinity and then as the consequence of an event or action became exalted into divinity by the Father later [?]
No and No - according to scripture, Jesus has always been divine:
1In the beginning was the Word, and the Word was with God, and the Word was God. 2He was with God in the beginning. 3Through him all things were made; without him nothing was made that has been made.
14The Word became flesh and made his dwelling among us. We have seen his glory, the glory of the one and only Son, who came from the Father, full of grace and truth. - John 1:1-3 & 14 NIV (emphasis added)
The 'Word' (who from the context is Jesus') 'was God' from 'the beginning'.
...or is Jesus divine as a consequence of his nature or identity?
5In your relationships with one another, have the same mindset as Christ Jesus:
6Who, being in very nature God, did not consider equality with God something to be used to his own advantage; - Philippians 2:5-6 NIV (emphasis added)