It is up to the developer to distribute the required DLLs along with the executable. The IDE can not do this as it does not know the exact DLLs you need, plus you need to read the relevent license agreements before you can distribute certain DLLs that your application may need. You can use something like dependancy checker to get a list of required DLLs.

You will need to rebuild the Qt library to get a static release, by default only shared library is available. Note that a static release requires a different (more strict) license agreement than shared library. Its therefore recommended that you use shared library unless you wish to purchase commercial license (for full terms, please read the relevent license agreement)

"Can't find access-point of procedure" means you are using the wrong DLLs. There are two sets of DLLs in the Qt SDK, one set for QtCreator and another for applications build with Qt. Use the other set and your application will run.