The DLLs "from some SDK" are the Qt libraries. Deploying these is no different to asking the end user to install yet another version of the .Net runtime in order for your latest Microsoft creation to run. The only difference being the user might already have a suitable .Net runtime install by default or from another application.

If you hold a commercial licence or are releasing your source under the GPL then you might find static linking useful. It comes with a range of limitations regarding dynamically loaded plugins that you may need to be aware of. Regardless of Qt licence some elements of Qt are only available under the LGPL, which imposes some other restrictions.
You start by building your own Qt libraries from source for static linking as described in broad terms in the deployment information linked above and the Windows-specific page.