"There's noone I would rather marry", says my girl,
"than you; not even if Jupiter were to ask me!"
That's what she says ... but what a woman says to her eager lover
might as well be written in the wind or in rushing waters.
I replaced the indirect discourse with direct, just to make it absolutely clear what she says and what Catullus says. cupido amanti is, as you suspect, indirect object after dicit
EDIT: Do you by any chance read German? Here's the translation from the Tusculum edition. It always impresses me how well the translator, Werner Eisenhut, is able to reproduce the metres, from hendecasyllables to elegiac disticha:
Keinen, so sagt die Meine, möchte sie lieber als mich zum
Gatten, da könnte sogar Juppiter selbst um sie frein.
Sagen tut sie's. Doch was ein Weib dem Liebhaber sagte,
All das kann man sogleich schreiben im Wasser und Wind.