options.set("min", "new Date(2013, 3, 15)"); // 15 apr (month-1!)
options.set("max", "new Date(2013, 5, 15)"); // 15 jun
final DatePicker datepicker = new DatePicker("datepicker", Model.of(new Date()), options);
form.add(datepicker);
FYI, Options.asString() is designed to convert a String (java) to its javascript representation (by enclosing it into single quotes).
What you need here is to pass an javascript object, not a javascript string, that why you need to simply write "new Date(2013, 3, 15)".
The JSON options will look like
{"min": new Date(2013, 3, 15), "max": new Date(2013, 5, 15)}