Liz,
Your seedlings look great. That is very exciting!
Yellow King is an herbaceous peony. I don't think it is very common. It is actually a pale pink single with a big yellow centre.
http://americanpeonysociety.or...
I discovered a bud on one of my three year old seedlings that I moved last week. Even after being transplanted, it sent up a bud. What a little trooper. Here is a picture (a terrible one
), but it shows the bud on the little thing.