You can use the quarter dimension attribute to filter just Q1 and put a filter on the year span you want in the where clause.
Select {[Measures].[EMPLOYEE Recordable Case Rate]} ON COLUMNS,
{[DIM TIME].[YEAR - QUARTER - MONTH].[Quarter].members } on 1
from [Model]
where ({ [Dim Time].[Year].[2006]:[Dim Time].[Year].[2012]}, [Dim Time].[Quarter].[Q1])
You could also probably figure out a way to get the year and do something with firstchild, but my answer above seemed quicker/easier.