How to add month and year dropdown to calendar month view
The Date module has a subproject called Date Views. Once that 
module is enabled, you can add exposed filters to your date fields. Setting the filter option Date selection form element to select will provide the dropdown selection widget for your date. 

Finally, under the Advanced > Exposed form > Exposed form style > Settings link there's an Autosubmit option that will submit the filter form upon date change.