I think it's because she has a well-honed ability to mentally compartmentalize stuff in her life.
The car--with the stench of death in it--is symbolic of Caylee's death. Therefore, by ridding herself of the car, in her mind, she's ridded herself of Caylee's death.
She seems to live recklessly for the here and now. She doesn't worry that the car might be found, towed, and taken by LE forensics. All she cared about is getting rid a reminder of the death...once gone, she could go party with her buddies and not think about it.