Yes, you can copy header & footers from one document to another, just like you can copy body content. To do that, you can:
• open the header/footer in the source document, then select & copy its contents;
• open the header/footer in the target document, then paste the copied content.
Headers must be copied & pasted separately from footers.

Note: Every Section in a Word document can display three different headers & footers - first page, even page, and primary. And a document can have multiple Sections. Where a document has multiple Sections, the simplest way of replicating the headers and footers for all except the last Section is to copy/paste the actual Section breaks.

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Cheers,
Paul Edstein
[Fmr MS MVP - Word]