How about "my everything"? But I guess that's very serious.
I have the same problem, in my language we use the same word for both girlfriend and girl and that word just sounds harsh to me.
Partner... I don't know. It's... well it won't hide the fact she's a girl cause my language is formed in a way that makes it impossible to speak non gender-ish. And it sounds like something I used in school, my lab partner, my dance partner, my skipping class partner...
As for pet names, I've been called kid (cause I'm like two years younger), little heater (I'll let your imagination work that one out), blondie (my hair is black though...), smartie (after nestle's candy). And I called her sweetest thing, charming, blondie (she is blonde!!) and slacker.
But pet names depend on your personalities.
"They say true friend knows song in your heart.
You're my song when I'm torn apart."
Lifetime, Me