jacek yes exactly!
I have found the solution!

When the custom request header is being constructed for GET request,
then all request parameters must be added there (to Path).
As a string like "?aaa=123&ccc=456"

QString strPath = RealURLPath;
if (GET == RequestType) Path += "?aaa=123&ccc=456";
QHttpRequestHeader* pHeader = new QHttpRequestHeader(RequestType, Path);

It should not be done for POST request.

Then we can send both POST and GET requests with custom header and request parameters through Qhttp::request() method.