I hope you find another bunny!!
My DD was also born 6/2003! DS is 4 now, and he never got attached to anything, but DD latched on to her brother's old "My Pal Al" toy and so we started letting her sleep with it. She doesn't carry it around -- in the morning she says "bye bye."
My mom tried to buy one for her house, but it had been discontinued and replaced with a new version with plastic/chewable feet. DD hated it! She liked old Al's felt feet and stroked her face with them. Kids are strange.
We took Al on a road trip to Florida last year and almost lost him a few times. I'm not sure how he made it through 6 different hotels/houses (long trip) but he did.
When we got home I realized how bad it would have been if Al had disappeared! I searched on Ebay and bought 3 more!! 2 were from the same seller and she probably thought I was nuts.
But now we have an Al for the crib, the car, grandma's and an extra. I think she needs him less, as she will sometimes take a doll or eeyore to bed now.