Can I have 'Query Store' automatically on when I create new databases?
Query Store is not active for new databases by default.

If you turn it on for model database, it will be on for any new databases you create in the same instance.  I tested in SQL 2017.

To turn it on in model database run following:

ALTER DATABASE model SET QUERY_STORE = ON; 


I suggest you read this article and decide if you want to turn it on for all databases and settings you want to modify.

Best Practice with the Query Store