Can I reactivate my Peggle Nights in-app purchase on my new iPad without being charged again?
iTunes Store: About In-App Purchases


  If you lose your In-App Purchases
  because apps were accidentally
  deleted, or if you had to restore your
  device without a backup, you may be
  able to download some of your in app
  purchases again for free. Not all
  In-App Purchases are eligible for free
  download again.
  
  
  Replenishable In-App Purchases and    subscriptions cannot be downloaded again for free, and must be  repurchased. Examples include but are not limited to: extra ammo additional health, extra experience points, or other one-time services. 
  Non-replenishable In-App Purchases    and auto-renewing subscriptions can be downloaded again for free. Examples include: bonus game levels a map/city guide, a daily news subscription, or other recurring  services.  
  To download an In-App    Purchase again, you must download it from within the installed app using the same iTunes Store account name for the original In-App Purchase.
  


It's an addon that is not limited, ergo a non-replenishable In-App purchase. So I would say it has to work.