She doesn't look like she belongs in a kidde grade.

There were lots of minor role girls in the anime and I don't know the names of at least half of them.
Have a nice day

She's one of the lead characters ^^;
For some reason the credit on the image is incorrect (is this from the FUNimation set?) - the artist is actually Bou Ditama (Mahoromatic) and it was correctly credited on the Japanese release (this card came with the 11th Collector's Edition DVD)
Dr.Moro's art looks nothing like this ^^;;;

This was one of the cards in a pack which arrived with one of the Kiddy Grade DVDs and the card set had no information.

http://gallery.minitokyo.net/view/22088/
in the bottom right corner, i (hardly) read:

- the kanji (the last character):
http://nihongo.j-talk.com/parser/search/kanjisearch.php?pick=4B3F
it means 'a certain person' (?)
- before it, the 3 hiragana are: ji'da'ma (is that a name?)
- and before the ':', the 4 katakana are: i'ra'su'to (= fanart illustration)

so, it says 'fanart by a certain Jidama' ? ...who is that?

Quote by deepflowhttp://gallery.minitokyo.net/view/22088/
in the bottom right corner, i (hardly) read:

- the kanji (the last character):
http://nihongo.j-talk.com/parser/search/kanjisearch.php?pick=4B3F
it means 'a certain person' (?)
- before it, the 3 hiragana are: ji'da'ma (is that a name?)
- and before the ':', the 4 katakana are: i'ra'su'to (= fanart illustration)

so, it says 'fanart by a certain Jidama' ? ...who is that?

irasuto just means "illustrated by" or "illustrator" - this is official art, not fanart.
Like I said a couple of comments above, the artist is Bow Ditama/Jitama Bou (????).