It may take 3-4 months to get your H-1b extension approval, so prepare accordingly. On the other hand, if there is any delay, the starting date of your new H-1b will be issued based on your company suggested date, normally the next day of expiration date of your previous one, so it will not be a big deal.
Having a peach mind, you may tell your company to prepare no later than August.
Just my two cents.