A family of Microsoft word processing software products for creating web, email, and print documents.
I see that you posted this question last week on StackOverflow and didn't get any useful answer. (It helps to mention that you're cross-posting, so people don't spend time if you've already gotten an answer.)
There is a way to do this with only an inline shape, by setting up a table to position the text on the left and the picture on the right. An additional advantage of this method is that, if you set the table's AutoFitBehavior property to wdAutoFitFixed and set the column width to the width you want for the shape, Word will automatically resize the picture to that width and keep the aspect ratio.
Here's a little sample macro:
Sub x()
Dim fpImage As String
Dim strExistingHeaderText
Dim tbl As Table
Dim shp As InlineShape
fpImage = "D:\Pictures\bunnycakes.jpg"
With ActiveDocument
strExistingHeaderText = _
.Sections(1).Headers(wdHeaderFooterPrimary).Range.Text
Set tbl = .Tables.Add( _
Range:=.Sections(1).Headers(wdHeaderFooterPrimary).Range, _
numrows:=1, numcolumns:=2, _
AutoFitBehavior:=wdAutoFitFixed)
tbl.Columns(2).Width = InchesToPoints(1.5)
tbl.Columns(1).Width = InchesToPoints(5#)
tbl.Cell(1, 1).Range.Text = strExistingHeaderText
'tbl.Borders.Enable = False
Set shp = tbl.Cell(1, 2).Range.InlineShapes.AddPicture(fpImage)
End With
End Sub