<xsl:template match="/">

That matches the root of the document, not the element that you have
confusingly called Root (which is its child) so 

	<xsl:apply-templates/>
applies to <Root> which recursively applies the default template to all
elements of the docuemnt.

	<xsl:template match="/">
		<Root>
 		<xsl:apply-templates select="Root/Header"/>
                </Root>
	</xsl:template>

would work, or simply

	<xsl:template match="/">
		<Root>
		<xsl:copy-of select="Root/Header"/>		
                </Root>
	</xsl:template>

David