Of course you do my love
my correct translation tells me: "Do I look equally as good as she". That sounds just weird!
I would say the -stejne...jako- has the same meaning as in English -as...as-
The correct English grammar is, "Do i look as good as she?" Basically you shorten the sentence, "Do I look as good as she does?" "her" is used in conversational English.
Why is it "jako"? Does it not refer to "ona", and thus should be "jaka"?
No. Jako is conjunction (like), does not change.