There is no option of exporting via GUI. You have to use API:
Using those endpoints from configuration API you will be able to get JSON representation of your dashboard. You can than post it to prod environment in the same way. But First you should be sure that all filters that were used on QA will exist on PRD. I mean for example tags (you can use configuration api for automatic tag rules as well: https://www.dynatrace.com/support/help/extend-dynatrace/dynatrace-api/configuration-api/automaticall...). But those tags will have different ID's so after deploying dashbord it may need fixes in this area. We are doing it like this sometimes, but most cases we are recreating dashboards on new enviornment (if they are not too big, or there is not to many of them).