This question is not actually answered in Looking for Alaska; it is left up to the reader to decide. However, there are ideas spread throughout the novel that can lead the reader to make up their own mind on whether Alaska's death was suicide or simply an accident.
For example, Alaska had started to make plans for her future again, so she still had hopes and dreams she wanted to fulfill. Also, she was determined to reach her mother's grave that night. These two facts alone show us that Alaska almost certainly did not get in her car planning on killing herself. We know she was distracted, thinking deeply about things; she was depressed, and possibly crying; and she was also drunk. Any of these things could lead to an accidental car crash.
On the other hand, Alaska was an incredibly impulsive person. Being overwhelmed as she was with sadness and guilt, it is easy to imagine her seeing the car ahead and just letting her own vehicle veer toward it without really thinking about it too much.
Based on these facts, it seems reasonable to conclude that Alaska's death was probably intentional, but likely the impulse of an emotional moment.