Dear Arno,

I'm going to take sides with your girlfriend. If my significant other called me "my little scatterbrain" I might pick up a frying pan and scatter what little brains he possesses. Then we would see who the real "scatter(ed) brain" was.
The problem with these so-called cute little nicknames is that there is an underlying bit of meanness connected with them, a subliminal need to pick at the other person. You might just be better off calling her "sweetie" or "Schatz", something neutral and more lvoing, rather than something that accentuates one of her foibles.

...
use "Dummerle"!

Every diminutive is supposed to sound cute.

BTW: is there a sylable in A/E like "le/chen/lein"?

OK, first of all, my girlfriend is not as aggressive as you obviously are... ;-)

No, seriously, I think I'm aware of "an underlying bit of meanness" connected with such a nickname, but in German we say "Was sich liebt, das neckt sich". Isn't that a common behaviour in the American culture, too?

Alright, I see your objection, but that's why I'm looking for a word which allows to banter with someone and isn't that "mean".

<OT> I appreciate how you care for other people's girlfriends, but don't you think that relationships are different and can't be generalized? Don't worry, I won't wreck her psychologically... <OT>

Butthead:

Thanks, but she doesn't speak any German, neither Swabian(?).

merriam webster:
Entry Word: scatterbrain
Function: noun
Text: a flighty thoughtless person <his wife is a scatterbrain>
Synonyms birdbrain, featherbrain, featherhead, flibbertigibbet, harebrain, rattlebrain, rattlehead, shatterbrain
Related Word fool, goose, silly, simpleton
I wouldn't call any of those words "cute".
I supose you could use scatterbrain sometimes, just to tease her - but as a nickname I'd prefer something else.

re: what merriam-webster listed as "related words"

It's not reeeeally a proper translation of scatterbrain, but calling someone a silly goose is quite cute and could be a borderline term of endearment. Someone who is a scatterbrain is all over the place, but perhaps based on an action they did which had lesser negative consequences, you could thus call them a silly goose for their silliness in not having thought through their actions. I've personally never gotten negative feedback from using it. I can't for the life of me imagine why M-W lists goose, maybe from the game we play as children 'duck duck goose'??

well, my girlfriend sometimes calls me silly goose even I don't consider having such a foible; but I look at it as an endearment...

However, I would not want her to translate that back into German, as "dumme Gans" is really different imho!

LEO translates "dumme Gans" with "dumb Dora" - no explanations on Dora, though???
Anybody knows where Dora comes from?