After checking I found that there is a problem with QProcess. I used SHELLEXECUTEINFO instead. This code works for me well. No recursive calls of phantomjs.exe here:
SHELLEXECUTEINFO shExecInfo;
shExecInfo.cbSize = sizeof(SHELLEXECUTEINFO);
shExecInfo.fMask = NULL;
shExecInfo.hwnd = NULL;
shExecInfo.lpVerb = L"runas";
shExecInfo.lpFile = L"phantomjs.exe";
shExecInfo.lpParameters = L"test.js";
shExecInfo.lpDirectory = NULL;
shExecInfo.nShow = SW_NORMAL;
shExecInfo.hInstApp = NULL;
ShellExecuteEx(&shExecInfo);