I'll take my best shot
I am not a network engineer, but I'll take my best shot. IP (Internet Protocol) is basically Layer 3 of the OSI model, which means it can run on top of Ethernet (or whatever your data link protocol is), and it can carry anything from higher up the networking stack. In practice, there are some additional complexities with higher-level protocols and applications, especially those that use IP addresses instead of host names, but a lot of applications should just work. The biggest problem is getting a significant chunk of network infrastructure to run IPv6. Not only does the protocol itself need to be deployed, but addressing schemes need to be vetted, routing and firewall rules implemented, and all the inevitable snafus need to be ironed out. Logistically, it's a significant challenge, probably more than it is a technical one, and it involves a tremendous amount of time and expense, and it requires IPv6 expertise that is not very widespread at the moment, which means that more mistakes than normal will be made along the way, resulting in reputational damage to the implementers.
Beyond all of that, there are plenty of endpoints that either don't run IPv6 still (think: printers) or run it poorly (Windows XP), which means that ISPs and other network providers will need to run in a hybrid mode, employing NAT or protocol tunneling, to support the legacy protocol until the final consumers make the migration. Which, of course, means that the consumers need to be educated and migrated, not so bad when you have a well-educated user base (or at least a captive and docile one), but daunting when you consider how many users will need to be wrangled into compliance and how few of them will even understand why.
So, it's not quite as hard as rebuilding the Internet, but it's still no small task.