SQL Server Query Store on isolated volume
No, as of 2018/04/25, you can't choose the filegroup where Query Store data is placed. In the databases where you enable Query Store, the data goes into the default filegroup.

It was a highly upvoted Connect item, so other folks share your pain - so I would expect that to be an enhancement added in the future.

Thanks to @klitzkrieg, here are the current feedback items:


Option to store query store data in a filegroup other than PRIMARY
Create central repository for Query Store