Here's a formula that will create a date field from the quarter. Note that there are more efficient ways to write this using some math instead of string manipulation -- if you have a large volume of data, you'll want to consider that approach.
Date(STR([Year]) + "-" +
IF [Quarter] = "Q1" THEN "01-01"
ELSEIF [Quarter] = "Q2" THEN "04-01"
ELSEIF [Quarter] = "Q3" THEN "07-01"
ELSEIF [Quarter] = "Q4" THEN "10-01"
You could also simply move Year to the Dimensions shelf and then create your own hierarchy of Year --> Quarter. You won't have all the options of the built in date dimension, but it would be simpler and more efficient if it met your needs.