A alternative:

   Selection.HomeKey unit:=wdStory
   If Selection.Sections(1).Range.ComputeStatistics(wdStatisticPages) > 1
Then
       With Selection.PageSetup
           .DifferentFirstPageHeaderFooter = True
       End With
   End If

This test to see if the first Section has more than 1 page; if it does, it
sets Section PageSetup Different First page = True.

You could also further explicitly make the header different text.  it is
important to note that Sections in Words ALWAYS have three headers -
regardless of whether there are Different first page, or Different Odd/Even.  
There is NO header for odd pages.  There are:

wdHeaderFooterPrimary (index = 1)
wdHeaderFooterFirstPage (index = 2)
wdHeaderFooterEvenPage (index = 3)

So you could do:

   Selection.HomeKey unit:=wdStory
   If Selection.Sections(1).Range.ComputeStatistics(wdStatisticPages) > 1
Then
       With Selection.PageSetup
           .DifferentFirstPageHeaderFooter = True
       End With
      Selection.Sections(1).Headers(1).Range.Text = "all other headersr"
      Selection.Sections(1).Headers(2).Range.Text = "firstpage"
   End If

This would explicitly insert text into the proper header.

Excellent!  Thank you both very much.

Penn