Now what?

 
The Girl had her heart set on planting her own carrots from seeds...and so she did (don't tell Monsanto).  I don't know why I didn't expect her seeds to grow...but I guess I really didn't consider that that they actually would.  A few days ago we started seeing hopeful little green stems sprouting up through the soil.  Now our question is...what do we do with these little seedlings? We don't have any garden beds this season, but we do have plenty of fairly deep containers.  Can you successfully container-garden carrots?   It's pretty cool to watch these adorable little sprigs reach for the sun outside the window.  At what point should she move the little plants to the bigger containers?  We thank you in advance for any carrot-growing guidance you can offer us.