What
evidence is there that it could work?
Each of the pilots seemed to be paired up with a female counterpart—Dorothy is the closest Quatre has.
When fighting near the end of the series, Dorothy realized Quatre was using the Zero system at the same moment he realized she was piloting the mobile dolls.
There really is no positive evidence in the show, other than the possibility itself. Quatre and Dorothy are very different people with nearly opposite personalities—on the surface. Internally, both have suffered from some very serious psychological problems in their life, both have lost close family, both lost their goals for a while. To Quatre, Dorothy is someone that desperately needs his help and support. He has lived through a difficult period himself, and therefore would have a lot of advice to give to her. To Dorothy, Quatre is someone to get her life back in order—she needs stability, and compassion after everything she's gone through.
What evidence is
there that it wouldn’t work?
She shot him and stabbed him with a fencing sword.
Quatre works better with Trowa (see their section)
In
Conclusion
For the non-yaoi fans, it's nice to pair each of the pilots up with a female partner, and Dorothy is the first person available for Quatre. However, these two don't have enough in common to work as a couple. It's obvious that Quatre is more interested in helping Trowa than Dorothy, and Dorothy simply expresses no personal interest in Quatre. Moreover, Dorothy already has some strange connection (if not attraction) to Trieze, or even Zechs (and maybe even Relena….@_@). This pair could definitely use the support of each other after the war, but there is little possibility of them ever becoming a couple.
