What are the negative consequences of taking doxylamine succinate and cetirizine together?

No, except: Doxylamine is rarely used nowadays and it does have some drowsiness effect as with all first-generation antihistamines. Since Cetirizine also causes drowsiness in roughly 10% of the people, you are more likely to get drowsy from taking both of these medications. Otherwise I do not expect any significant problem with side effects.

Possibly: If you use them together, they will each make the other's sedative (sleepiness) effect worse. This could hamper your ability to drive or concentrate. Be careful about how you use them together. Generally you should probably avoid them together unless there is a strong need and your doctor is supervising.