I don't see how this:
Fist problem is that my qt creator doesn't know qextserialport.h.
is related to this:
You can try the ready module: QtSerialPort
They are two different components. QtSerialPort is a part of Qt 5.1 out-of-the-box, QExtSerialPort is external.

You use external libraries by including the relevant INCLUDEPATH and LIBS entries in your PRO file.
Declaring Other Libraries

And why do you use dataTerminalReadyChanged(bool) signal? I need only set DTR on push button, so should I just call onDtr() function in push_button case, right? I don't need connect(port, SIGNAL(dataTerminalReadyChanged(bool)), this, SLOT(onDtr(bool))), do I?
The signal dataTerminalReadyChanged() signal connection ensures that regardless of how DTR is turned on the timer is started. The connection to the timer signal ensures that DTR is turned off approximately 50 mSec later. You can arrange it differently if you wish.