There's no reason to book super early for those dates. Although Christmas itself may be busy, otherwise it's during the slowest weeks of the year. Hotels will have vacancy. Cars will be available. You'll find a seat at your favorite machine or table.
First and foremost, book directly with the hotel, airline, and car rental agency. Do not use a third party or you will lose your flexibility.
Get air first, since you're traveling near a holiday. Look for the next SWA super sale. These sales occur fairly often. I received the same SWA email Dan mentioned. Contact SWA so you get the next one. Once those dates open up, book the cheapest convenient flights within your travel window. Don't wait. Cheap holiday fares go fast.
Once you have your flight, book the car. DO NOT PAY IN ADVANCE. Reserve with one or two agencies. You will be checking back with car rental agencies from time to time and will cancel and rebook as rates fall. This can continue right up to a few weeks before the trip. EZ and Fox are okay, so long as you don't mind being inconvenienced at the counter and getting a not very new, not very clean car. Oh, and Fox gives you an extra bus ride, too.
Hotels will have vacancy and good prices. Shop around and book something, but once again, DO NOT PREPAY and be prepared to cancel and rebook if a better deal comes along. If you'll be out of town overnight, this can work in your favor with booking because Vegas is geared to shorter stays. Shoot, you might even swing some free nights for part of it- maybe one place before Cal and another after. If possible, visit your friend on a Friday or Saturday night because Vegas hotels cost more on those nights.
Shows are harder to book for that week because some of them will be on vacation. What you can get and how you get it depends on numerous factors, but the main thing is that booking a show involves a monetary commitment, so be sure what you book is what you want. Maybe winter would be a good time to try a half-price booth after you get into town. For my money, the best show in town right now is Human Nature, the four Aussies who sing Smokey, if you like that.
Some restaurants will also be closed. There is no lack of food opportunities in Las Vegas, though, and you can probably get in almost any place that is open by calling the same day.