JACKSON: Uh, hey, do you wanna look at the Brussels sprouts?
SOOKIE: Yes, I do. [giggles] No. Ooh, what about some nice Brussels sprouts with like a garlic olive oil for the wedding? That sounds like a “‘Til death do us part” kind of side dish, doesn’t it?
Sookie says “I do”, which is the traditional way to agree to marry someone in the wedding vows, and “… until death do us part” is the conclusion to the traditional wedding vows, which date back to medieval times and are printed in prayer books.
Sookie is just teasing Jackson, but later they will be married for real.
The Annotated Gilmore Girls 