You don't even need to identify the section number e.g.
Code:
Sub CopyCurrentSectionToNewDoc()
Dim rng As Range
Dim NewDoc As Document
Set rng = Selection.Sections(1).Range
rng.End = rng.End - 1
Set NewDoc = Documents.Add(Template:=ActiveDocument.AttachedTemplate.FullName, Visible:=True)
NewDoc.Range.FormattedText = rng.FormattedText
End Sub