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Is your laptop a Chromebook? having no hard drive, sounds rather like a Chromebook.
If you, you need to have your QL700 connected to Google Cloud (an internet service requiring, of course, an internet connection).
That may be rather difficult for you, or disappointing to your expectations, unfortunately. Connecting a printer to Google Cloud requires that the printer be Cloud-ready (in other words, that it be on a list that is limited in size, of Cloud-ready printers) or else that it be connected to the Cloud through a Windows PC or Apple computer.
Is your Brother QL-700 a Cloud-ready printer? unfortunately, it is not, according to the list shown here:
So it would seem that you will need for it to be connected to the internet and the Cloud through a Windows PC or an Apple computer.