The extension should be enabled by default if being used through ArcGIS Pro:
When say logging into the Developer Account are you referring to MyEsri or ArcGIS Online? Are you just looking to get started using the tool or just to view the licenses assigned to you?
The extension should be enabled for you automatically. Can you log into ArcGIS Pro and try the two following steps?
We had not luck with that. I had her, in Pro, log into https://arcgis.com using her professional developer account and try and check out image analyst and it was till grayed out. Do we need to connect accounts or something?