Contacting supervisors directly is a good idea and show initiative. Though I wouldn't send them a full-blown proposal in the first email, maybe say you are working on one and say what it is about. It looks good that you are thinking that far ahead but you don't want to be to pushy (or they steal your idea). If they are interested they will ask about it and then I would send it over.
Also, a lot of supervisors have ideas/projects that they are interested in but don't have funding yet. They might direct you towards them but don't be forced into one just for the sake of a PhD.
Goodluck!