You could use the qsvariable extension from qlik branch to achieve this functionality. This will allow you to populate a variable you create via a form object, either input box, drop down or slider which you can then use in your charts via set analysis to set a user defined date range.
To start off with setting a default value for the variables you want to use.
Apply them into the charts you want them to work with using set analysis.
Then go from there with your qsVariable extension.
I've attached an example where Ive used this approach myself although its not a date example the principle is the same.