The Qt window you created with Qt Designer appears in Maya once you load a .ui file with the loadUI command. However, this window acts as a separate window from the Maya main interface; for example, if you minimize Maya, the Qt window is not also mininized. To make the Qt work more consistently within Maya, you can parent it under one of Maya's window using the following script:

$w2 = `window`;
$p = `paneLayout -configuration "single" `;
control -e  -p $p $dialog1;
showWindow $w2;