A good time to start looking to rent again would be no later than a month or two out from when your lease is up. That gives you time to find the right place and organize all the finer details it will take.
I know you said you were not ready to buy yet but did you know that you could possibly get a mortgage payment for close to or below what you would pay for rent? Mortgage rates are still at record lows and prices are only going to increase here in AZ.
Since you have a lease until November, my advice would be to talk to a mortgage lender to see how much you could qualify to buy a house for and see what your payments could be like. That way you could own a house and build equity instead of throwing away $800-1000 of rent each month. Check out my website and visit the blog to see how I break down "Renting Vs. Buying".
If you don't like the options after talking to a mortgage lender and want to rent then that is okay too. I would be happy to help you find a place to rent. I also have a great mortgage lender contact that you could speak to. Feel free to call me anytime to discuss :)