A pre-nup or prenuptial negotiation is something which a couple may do before they get married to each other. The idea is that they discuss what happens if they were to get divorced sometime in the future. They might discuss how to divide their possessions/money and who gets to look after the children etc. After the negotiation they sign a pre-nup agreement, which is a legal contract.
In this context, Mel is irritated because she feels the man is being too cautious - they're only going on a date, it's not llike they're planning to get married!
Hope that helps