Make sure the insertion point is at the start of the document.
Turn on the macro recorder.
Use the keyboard to navigate to the spot where you want the date.
Stop recording
Copy that code and paste it into the code you already have.

Okay Kim, just tried that to no effect. Copied and pasted the code as follows:

Sub Macro2()
'
' Macro2 Macro
' Macro recorded 28 September 2010 by Trainee
'
Selection.MoveDown Unit:=wdLine, Count:=24
Selection.MoveRight Unit:=wdCharacter, Count:=37
End Sub

And pasted that at the start of my existing code. It had no effect whatsoever, the document still opened at the very beginning, and that's where the date is inserted as well.