Hello there, I'm Dr. Sara - I'm a dog and cat vet AND a mom to two small children, so I can definitely relate to the diaper eating issue!!!
Believe it or not, the diaper is fairly nontoxic, so I don't get too concerned about any sort of toxicity. This type of ingestion can certainly cause some GI upset which could come in the form of vomiting (I know, right, EWWWW!) or diarrhea within the next few moments to a day or two from now. For the moment I would just monitor your pet for any signs of distress. Most labs have stomachs that can tolerate just about anything, and many times they eat terrible things and we never know because they do absolutely fine. My own beagle has pulled this on me MULTIPLE times - sometimes he vomits (which is gross) and sometimes he doesn't.
If you had recently used any sort of diaper cream containing zinc (like Desitin), this might make your pet a little more likely to vomit tonight. Zinc is toxic can can cause anemias, but usually it makes them nauseous enough that they vomit most of it up and don't become ill from zinc toxicity.
For tonight I would just keep an eye on your pet, knowing that you might see some vomiting. Be prepared for a yucky cleanup. If he/she seems like they are in any sort of distress, are vomiting more than a few times, or if you see any abdominal distention, I would consider seeking care at your nearest veterinary ER.
I sure hope that this information is helpful to you - please let me know if you have any other specific questions I can answer!