The queries in the Query Editor of PBI Desktop are to establish the fundamental data sets/model needed for the reporting goals.
In PBI I don't think of a single discrete query object as one has in a database in terms of a sql statement - but rather modeling is typically a series of steps to add calculated tables/columns to establish the data model. So copying at this level isn't usually a question that is asked.
Once the core data sets/model is established then a wide variety of reports can be built from them, and then in turn a wide variation of dashboards can be created using pages from a variety of reports.
If you have alot of parallel table data sets - which would cause you to remake the same reports repeatedly but oriented to different table - if their table stucture is identical you would want to consider consolidating them into a master table so that a single report with filtering can be used.