Declare Variable for a Query String

It’s possible, but it requires using dynamic SQL.
I recommend reading The curse and blessings of dynamic SQL before continuing…

DECLARE @theDate varchar(60)
SET @theDate=""'2010-01-01'' AND ''2010-08-31 23:59:59'''

DECLARE @SQL VARCHAR(MAX)  
SET @SQL = 'SELECT AdministratorCode, 
                   SUM(Total) as theTotal, 
                   SUM(WOD.Quantity) as theQty, 
                   AVG(Total) as avgTotal, 
                  (SELECT SUM(tblWOD.Amount)
                     FROM tblWOD
                     JOIN tblWO on tblWOD.OrderID = tblWO.ID
                    WHERE tblWO.Approved = ''1''
                      AND tblWO.AdministratorCode = tblWO.AdministratorCode
                      AND tblWO.OrderDate BETWEEN '+ @theDate +')'

EXEC(@SQL)

Dynamic SQL is just a SQL statement, composed as a string before being executed. So the usual string concatenation occurs. Dynamic SQL is required whenever you want to do something in SQL syntax that isn’t allowed, like:

• a single parameter to represent comma separated list of values for an IN clause
• a variable to represent both value and SQL syntax (IE: the example you provided)

EXEC sp_executesql allows you to use bind/preparedstatement parameters so you don’t have to concern yourself with escaping single quotes/etc for SQL injection attacks.