from PyQt5.QtCore import QDate
from PyQt5.QtWidgets import QApplication, QWidget, QVBoxLayout, QDateEdit, QPushButton

def btn_clicked():
    date_text = '2011. 11. 13.'
    date.setDate(QDate.fromString(date_text, 'yyyy. MM. dd.'))

app = QApplication([])
window = QWidget()
date = QDateEdit()
btn = QPushButton('Gomb')
btn.clicked.connect(btn_clicked)
layout = QVBoxLayout()
layout.addWidget(date)
layout.addWidget(btn)
window.setLayout(layout)
window.show()
app.exec_()