Months. Traditionally a change like this saw little enthusiasm or interest, and had a very slow uptake, because it didn't add value until all of the players changed. Now, however, browsers iterate so quickly that already there is HTTP/2 support on the majority of user desktops. If you run a Go or node.js or various other technology websites, even if you "self-host" HTTP, you likely (and should) have it behind nginx or Apache or HAProxy, and all of those are quickly implementing HTTP/2 (or more correctly changing the existing SPDY functionality to the final spec. And for those who wonder, a HTTP/1.1 Go app sitting behind a HTTP/2 proxy still delivers HTTP/2 benefits to the end user). Cloudflare had SPDY support over two years ago, so I expect they'll see very quick support.

Of course, and you addressed this, this doesn't mean that HTTP/1.1 disappears. Heck, my web properties still see HTTP/1.0 requests, almost a decade after HTTP/1.1. But that is a very small minority.