Perhaps I miss-read. I thought you meant your label stationery had a header with the date. If it's only the data source that has that, you could either:
• add a column to the data table, then add both a column name (eg 'DATE') to the table's header row and insert cross-references in each cell pointing to the bookmark. You can then reference the new field (column) in the first label in the mailmerge main document; or:
• insert an INCLUDETEXT field into the first label in the mailmerge main document pointing to the bookmark in the datasource.
In either case, once you've updated the first label, clicking on 'update labels' should then propagate it to all labels.

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Cheers,
Paul Edstein
[Fmr MS MVP - Word]