The issue with your document is that you have formatted the table with 'around' text wrapping. It would have been helpful if you'd mentioned that. Try:
Code:
Dim bShow As Boolean
With appWord.ActiveDocument
bShow = .ActiveWindow.ActivePane.View.ShowAll
.ActiveWindow.ActivePane.View.ShowAll = True
.Sections.Add Start:=wdSectionNewPage
.Tables(1).Range.Copy
.Characters.Last.Paste
.ActiveWindow.ActivePane.View.ShowAll = bShow
End With