Is it reasonable to apply for (postdoc) positions early?
My recommendation is first that you don't worry too much about it, but I think there is an important exception: if you are applying using MathJobs, then you should apply once you have your documents ready, hopefully at least a couple of days before the deadline.  In particular, you should not wait for your references to add their letters if that is the only thing you're waiting for.  Those will show up when they are available, but it's much better for someone to see your application is there without all the letters, than for you to get lost right in the avalanche when everybody else submits right at the deadline.  Similarly, you can update your CV, so there's no reason to wait in hope of another paper to getting accepted.