Finished? Painted? Unfinished? Smooth? Rough? How big?
If you haven't already gone to the ER, please do so ASAP.
After the docs have got it out of her, or after they have instructed you
on what to do to help get it out of her, depending on its size and description, please look into getting some family counseling.
An eight-year-old child KNOWS BETTER THAN to swallow a piece of wood.
It occurs to me that she might have done this intentionally for attention.
Eight is an age where a child can reason, can consider consequences.
Did she tell you about it only after 12 hours?
Did she tell you HOW (or why) it happened?
If you don't already have good communication between you,
you need to start working on that ASAP.
She's JUST heading into the age where you'll want her to trust you,
to know you're a safe reliable resource for her
as she goes through the upcoming changes.