Dawn,
I am half way into making this cake. Its cooling. Caryn was right about blanching the carrots. I put big carrots in boiling water for 3 minutes and tiny baby carrots for almost a minute, then plunged in ice water. I made the flowers from the big ones, and since my daughter insisted on sprinkles, I made confetti by cutting the baby carrots into hole-punch sized confetti sprinkles.
Also, I took some of the icing, added some safe yellow dye (turmeric, I think) and packed it into an old medicine dropper so I could put a perfect little yellow center in each flower. It was a lot easier than getting out the frosting bag and tips because so little was needed.
I haven't tasted it yet, but it looks good in its egg-free form. I used 4 Ener-G replacer eggs and two smushed bananas. (Caryn mentioned using extra when replacing, so I hope that covered it.)