They'll have seven days to recover from victory over Antrim.
Laois will face Waterford in the All-Ireland Hurling qualifiers next weekend.
The tie has been fixed for Saturday with a time and venue to be confirmed at a later stage.
It's their first meeting in the championship in seven years.
This morning's draw has also paired Clare and Wexford against each other, while Cork and Galway have both received byes into round two.
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