Hi Sake, welcome to the forum,
I think you are right about the title being "Day of the Dandelion"
From the link you sent us for that face book page they said ghasedak. I googled ghasedak and cartoon and got a lot of pictures of dandelions including this little guy:
who looks very similar to your guy. This little guy belong to a blog post here: http://golpaart.persianblog.ir/1386/1/18/
The blog includes a link: http://forum.persiantools.com/showpost.php?p=1079291&postcount=931 the link mentions Day of the Dandelion as well. I've also been using this Persian translator, http://translation.babylon.com/Persian to translate a few things that everyone has been talking about on these pages if you would like to gather some more information from them.
Also, if you check out the form post that I included and click on "Arianna's Files" Arianna has actually uploaded the song. You'll have to navigate to the song (entitled Ghasedak) but it's all in english so you shouldn't run into much problems.