Use Keychain on OS X etc. for password storage
Please use the platform's mechanism for storing passwords if it provides one. E.g. on OS X, passwords should be saved into Keychain.app, on Gnome into Gnome Keyring etc.
If possible, it would be best to directly use the password database entry that a web browser created for the website mojedatovaschranka.cz so that the password would be saved in a single place and changing it either through qdatovka or the browser will update the password the other software is using too.
I found a project called qtkeychain (https://github.com/frankosterfeld/qtkeychain) that seems to provide platform-independent API for platform keychain functionality in Qt style, but I am not sure if it does not bring arbitrary restrictions (i.e. it might not be possible with qtkeychain to access password saved by a browser in a situation where that would be possible using the native API of the platform - speculative).