You can definitely do a one way rental, but it will cost you much more than a rental where you drop off the car at the same place you picked it up. Also, you'll have to go with someone other than Enterprise. They do limited one way rentals, but only within a metro area... they definitely won't let you take the car from LA or MS to FL.
Just for fun, I plugged your dates into the Budget web site and came up with a cost of $551.24 to pick up a minivan at the New Orleans airport on December 31st and drop it off at the Orlando airport on January 2nd. That's about right for a one way minivan rental for two days, but you might be able do a little better than that if you shop around a bit.
Also, since you've never rented a car before, here are a couple of quick points... For the most part you need to be over 25 to rent a vehicle. Many companies will allow you to rent a car if you're over 21, however they usually tack a daily underage driver surcharge... often as much as $25 or $30 per day.
Also note that by default only the person who rents the vehicle will be allowed to drive it (If someone else drives it and gets into an accident the insurance may not cover it, so be very careful about this). Normally this isn't a problem, but since you have a 9 hour drive you might want to switch drivers. You can add additional drivers when you rent the car, but they will all need to be at the counter with you and show their driver's licenses. Additional drivers fees can vary, so if you plan to do this definitely shop around. I've seen them as low as $3 a day and as high as $15 a day. If you have two companies with similar rates then their additional driver fees may make the difference. Also, each person added as an additional driver will need to be over 25 as well (or over 21 if you want to pay the underage driver surcharge)
Many rental car companies are now requiring you to use a 'real' credit card and not a debit card with a mastercard or visa logo to rent the car. If you don't have a credit card that you can use (note that they'll usually charge you the full cost of the rental, plus a deposit that can easily be $200 or $300 additional) then make sure that the company you rent from takes debit cards. Also note that when you use the debit card that the cost of the rental plus the deposit amount won't be available during the time you use the car, plus it usually takes a few days after you return the car before the deposit hold is cleared from your card.
Finally, refuse all of the extra insurance and gas options they offer to you. You might want to check with your own auto insurance company, but I've never seen an auto policy that won't cover you in a rental car, so the extra money for the rental insurance is just extra money you have to pay. They sometimes try to bully you into taking the extra coverage, but it's really not worth it.
The gas options they offer are usually a bad deal too. They'll offer to let you buy gas at a low rate (usually less than you can get it on the street for), but the catch is that you *have* to buy a full tank from them. Even if you return the car with 3/4 of the tank full you'll still pay for a full tank's worth of gas. That makes any small savings on their per gallon price worthless.
Finally note that rental cars are charged by 24 hour periods. If you pick up the rental car at 3PM on one day, then turn it in at 6PM two days later, you'll actually be charged for three days because of those extra three hours. Make sure that you can turn it in at or before the time you pick it up.
HTH,
Brett
