I don't think I've ever heard of anything like this in the "traditional" D&D settings, but not many of these ever go too hugely deeply into the culture of kobolds in their worlds, and I'm not a huge canon expert on any of them anyway, so I could be mistaken.
If you're not in one of the traditional settings, though, then anything goes. Honestly, even if you are in one of the traditional settings, the DM might have ruled on this one way or the other, especially if that setting was silent on the particulars of kobold courtship ritual.
Truth be told, I doubt that your DM actually intends for your character to go through with marrying a kobold. This is more likely just setting up for some culture-shock silliness.