I agree with the sentiment that Alice, as a child, thrown into a confusing and frustrating new 'reality', its hard to judge too much. I think the idea of Alice as a villain is really interesting though (I would like to that type of adaptation, a new person enters your world and interferes), but I digress
The Queen of Hearts to me seems to be the most obvious choice of villain and therefore it's easy to foist that title upon her. Yes she is tyrannical, she may or may not have reasons (she is a woman in a primarily male kingdom, she may not want to appear weak!) and her actions are not excusable, but I do think because she's easy to blame, we miss out on the real villain of the story!
I think you're right Astrid when you say that the Cheshire cat 'wants to see action' but I think he's more than just a troublemaker. He has no regard for the danger caused by or who gets hurt in the action, he knows very well that the queen has a penchant for beheading people and sends a lost child her way. He seems to enjoy the confusion, unhappiness and potential harm of others with no sign of remorse or empathy. Traits like this in people tend to suggest psychopathy! Not only that, Disney, who created the animated adaptation of Alice in Wonderland, classed him as a villain merchandise wise, along with the likes of Ursula and Scar.