Build a static Qt and static versions of any other libs you use, and build your application with that: see Deploying Qt Applications. The executable may be the as large as the original executable and all the associated dynamic libraries and plugins... it depends on what you use. If you are using the LGPL Qt, or any LGPL component of the commercial Qt, then your static executable will have requirements regarding relinking imposed by the licence. Other libs may impose other restrictions.
IMHO it is far easier to write an installer that puts the needed Qt libs in the same directory as the executable (not system32).
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