Is the Developer Dashboard available on SharePoint Online (Office 365)? How do you enable it?
According to Nik this is not possible link to source:
Developer Dashboard is not available in SharePoint Online for customers. SharePoint Online doesn’t have great story regarding Error logging and Monitoring. You can write custom framework which would log errors in the SharePoint list but you can’t have much control over ULS Correlation ID. If you are getting errors in OOB configuration, only way to resolve issues is working with Microsoft Office 365 Support team and supplying Correlation ID to the support team.
Correct, it is not available in SharePoint Online. I would expect the primary reason is that it is a farm level setting. This means that if you were able to turn it on, every customer that shares your environment would also see the update.