Hello J.! I have two suggestions. I agree with the other moms that perhaps the washing machine might work just fine. Also, I THINK your child might be over the eating stage...if you're fairly certain your children won't be chewing on the bunny, I found that repeated applications (WITHOUT RINSING EVEN!!!) :D of Bissell Pet Pro (or Pro Pet? it's a pink-labeled, double-barreled aluminum can, found by the vacuums in Walmart) worked to get male cat urine out of my daughter's hiking backpack. I SWEAR by this stuff now!!! I just set the backpack outside for about 10 days in South Carolina this past winter and sprayed it once or twice a day, and let it dry, and now there is NO ODOR. I promise you, I would have thrown that thing away a long time ago if there were any trace of the smell left! But you might just stick to the washing machine first. ;)
Best of luck,
K.