Disaster recovery server in a cloud

The key issue in a DR scenario is network performance between the instances.

You will run most likely an Async Mirror to have a reasonable distance between production and DR site.
I wouldn't suppose enough bandwidth for a sync Mirror.

The other issue is the performance of the DR site.  You require enough performance to process all the synchronization within a reasonably short delay. This is often underestimated, Production servers grow and leave their DR site behind.

Not specific to the cloud but not less important: How can you verify that the content of your DR site is really identic to your production.
For a heavy transactional operation, this can be a real tricky exercise.

And last not least if you don't train your team for a disaster situation and verify your instructions step by step at least once a year all your investment could be wasted money.

Especially this last point is skipped quite often as it means in most cases a lot of effort with no immediate ROI.