You found the solution yourself, why don't you use it?
Just calculate the boundary dates for the quarter in question and use them with BETWEEN
:
SELECT CustID
,CustName
,CustPhone
FROM SalesData
WHERE OrderDate BETWEEN '2012-01-01' AND '2012-03-31';
You can calculate the boundary dates in your application, or also via MySQL as shown in this article:
http://use-the-index-luke.com/sql/where-clause/obfuscation/dates?db_type=mysql