Is it okay to wear shoes half a size too big?

As long as you feel that they are the right fit for you, then yes. I remember when I bought my first real pair of climbing shoes after my beginner shoes, I tried downsizing as everyone had told me I have to, but even the salesman asked me to not downsize because the it just didn't fit me properly. What ended up being a "performance" fit for me was actually my street shoe size. This is in spite of everyone telling me I have to downsize to the smallest size that I can stick my feet in, regardless of the pain. So as long as you don't listen to that advice and you get what ever you can climb in without terrible pain, or without any pain at all, it should be fine.