Car rental at Christmas

[wayneg]

We are arriving at Orlando int Christmas day afternoon. A few years ago we did the same and prebooked car thru Alamo. They had overbooked and had no cars available, paid for us a taxi to Disney resort then another back to the rental lot the following day when they had car ready but a lot of hassle.
Is this common for Christmas? I would prefer to use Dollar, has anyone had same problem with them?
Wayne