As someone who taught high school for ten years, and who just just completed a doctoral dissertation using Q Methodology, one of the ways I imagine you could put this together is:
There is a TON of literature on teacher stress. Just thinking back to my own experience, issues such as motivation, burnout, standards, high-stakes testing, feeling inferior, feeling unsupported, family/career balance, challenges with peers, stressful students, etc.... I think just by doing a thorough lit review (as I'm sure you have), you could come up with 40 - 50 statements easily. Heck, I could probably give them to you! As you brainstorm, put all of the statements into an Excel spreadsheet or other software you use for keeping track, code them according to theme, and then have some teachers look at the statements. You could find out pretty fast if you are missing anything.
Then, as you work with your set of statements, think about your research questions. One of the things that helped me immensely was checking out 20 or so dissertations from the school library that used Q or used needs assessment (that was my topic) to see how others have written the research questions. I also feel the Watts and Stenner book helped immensely in visualizing my project. There is a ton of great lit on the qmethod.org site to guide you. Eliminate statements that are too similar, or that hit the same theme. Figure out how many statements and in what distribution you want your Q Sort to look like. I would pilot your Q Sort on a small number of teachers, to see if the sort works, or if anything the teachers find out of place should be corrected.
Do you have a specific set of teachers you want to work with? Purposefully choosing your sample of teachers is appropriate in Q. In my study, I worked with teaching assistants in the Biology Department at my university. I wasn't looking at every teaching assistant in the USA - too big a P Set - but I purposefully chose this set of TAs because they were who I wanted to help improve their teaching and support.
I imagine that you will come up with between two and four "types of teacher stresses" or "types of stressed teachers." At that point, after the analysis, I would give an exit interview to these teachers which asks for their input on coping mechanisms, professional development, or support systems that could help each of the types of stressed out teachers. Maybe some teachers need a forum to discuss their stress, small groups that meet at school to talk, or a teachers lounge that is inviting and soothing. Maybe other types of teachers need individual therapy, because their school stresses are a manifestation of their own personal problems. Maybe a third type of teacher needs a professional mentor who is a veteran teacher. There's a world of support systems out there - it's figuring out which teacher needs which type of support. In my dissertation, I found three types of TAs. All of the TAs in my sample needed a basic instructional training program, but then each of the types of TAs needed their program scaffolded to address their particular needs. I called it "additive scaffolding," and am writing an article about it now.
If you'd like a copy of my dissertation to see how I laid out my problem and research questions and Q Sort, I can send. I think you've got a great idea for a dissertation, and there are certainly a lot of ways you can approach this. I like brainstorming like this :) Also remember that what ever you propose will change dramatically when your committee gets a hold of it. Use the professionals around you, and in the Q community to explore.
Best of luck,
What are some other types of teacher stress, and what could your school have done to better support you through stressful times? Is there a way your could have approached stressful situations better? Would professional development have helped you better approach stressful situations? Are there online resources you use? I'd like to hear from teachers what kinds of things could help?