You want to getMonth/setMonth
var p = '2015-10-21';
var myDate = new Date(p);
myDate.setMonth(myDate.getMonth() + 3);
Don't worry about overflow - Date object handles it
Note. This overwrites myDate, if you want the result in a different var
var p = '2015-10-21';
var myDate = new Date(p);
var result1 = new Date(myDate);
result1.setMonth(result1.getMonth() + 3);
as noted by @JohnHascall in the comments, this isn't fool proof around the end of month, for example adding three months to 30 November 2015 will result in 1st March 2016