The official word from Canon USA is that the Canon EOS R body will begin shipping on October 9, 2018. This is also the scheduled ship date of the Canon EOS R/RF 24-105mm f/4L IS kit as well.
We've also heard reports that retailers will begin shipping Canon EOS R body only packages to customers today, though we haven't been able to confirm that with the retailers in question.
Win a Canon EOS R:
If you can't swing purchasing one right now, you can try to win our giveaway form a Canon EOS R body here.
Initial stock will be very good, so all preorders should be met. If you didn't preorder, now would be a good time to do so.
Canon EOS R Camera and Kits