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.
Offaly GAA Community Mourning The Loss Of Former County Chair
Ollie Daly died on Thursday after struggling with illness.
Town Looking To Bring Clean Sheet Run On The Road
The Westmeath club are heading to Tralee this week.
Dalton Starts For Ireland V England
The Leinster centre is one of two changes to Scott Beamand's side.
Joe McDonagh Cup: Laois v Offaly - Manager's Preview
Willie Maher and Johnny Kelly join Midlands 103 to look forward to this weekend's Championship opener.
Lowry Set To Take On RBC Heritage After Testing Masters Experience
The Offaly golfer finished in tie for 43rd at Augusta last week.
Everything Building Up To Joe McDonagh Cup - Joe Fortune
Westmeath get their campaign underway this weekend.
Egan, Pearson, And O'Neill Recognised In Team Of The Week
Declan Kelly's side face the defending All Ireland champions in the Leinster semi-finals next.
Westmeath Star Robbie Henshaw Opens New Vision Ireland Store
The rugby superstar is encouraging everyone to 'Skip the Skip.'
Henshaw Basking In La Rochelle Afterglow
The former Buccaneers player is thrilled to have overcome the defending European champions.
Laois Ladies Steel Themselves For Testing Senior Championship Campaign
The O'Moore County were relegated to Division Three this season.
Offaly's U20 Football Season Ends On Disappointing Note
Carlow ran out convincing winners on their SETU grounds on Tuesday night.
Laois Under-20s Fall At Quarter-Final Hurdle
The O'Moore County left Ashbourne with a defeat.
Women Leading The Way In Weightlifting - Ailbhe Mulvihill
The Irish athlete believes women are leading Irish weightlifting forward.
CCFL: St Peter's Close In On Senior Division Leaders
Willow Park remain clear at the top of the standings.
"You Have To Stick With Lads" - Declan Kelly Stands By Young Players
Offaly have suffered from inconsistency through the season so far.
Laois U20 Hurlers Lie In Wait For Westmeath
Westmeath take on Carlow in Mullingar in the first knockout round in Leinster on Friday.
Offaly Minors Progress Despite Dublin Loss
Laois finished their campaign on a winning note while Westmeath lost their third consecutive game.
"We Needed A Performance And That's What We Did" - Howe
Athlone Town secured a 3-1 win over Peamount United over the weekend.
Laois Hoping To Secure Semi-Final Spot In Clash With Meath
The O'Moore County are travelling to Ashbourne today.
HRI Confirm Cancellation Of Kilbeggan's Season Opening Two Day Meeting
The news comes after the sudden death of racecourse manager Paddy Dunican.
