Now is the time to start looking for jobs in September. Most schools like to have their new hires lined up before they leave for summer break. Also, a lot of schools start at the beginning of September so want you there in late August. If at all possible,you should look into trying to arrange things so you could do this as it would really open up your options.
I would recommend using TeachAroundTheWorld.net to look for jobs as they require all the job postings to put in a start date, so you'll always know when the school wants you by. I'm also looking for a job to start in the new school year and they have lots with start dates that I think would work for you. Good luck with the search!