I would just take a taxi to the Contemporary Resort and walk over. Then after the party, walk back to the Contemporary, and they'll get a cab for you. It should be cheaper than renting a car. If you ask the cab to take you to the Magic Kingdom, they'll take you to the TTC and then you'll still have to take the monorail/ferry to the MK.
Like Fran said, the hotel may have a free shuttle that takes you to the MK (though since it's on Universal property, I'm not sure), so check that out first. That would save you money for having to get there, but I'd still take the cab back after the party.
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