Erin Stellato link to two feature requests for Query Store:
Two of these requests have Connect items, which I’m listing below. The first allows you to change the location of Query Store data to reside somewhere in the user database besides the PRIMARY filegroup:
Option to store query store data in a filegroup other than PRIMARY
The other request is related to exporting that data, which is technically possible now, but it’s not a supported method so it’s not something I really want to implement in a client environment. I’ve had many people describe their process for testing which includes restoring database nightly. If they’re using Query Store as part of testing, that data is lost every night by the restore.
Export Query Store tables separately from the database tables
Click through for more and vote up those items relevant to you.