something like this?

https://en.wikipedia.org/wiki/IP_over_Avian_Carriers

That would be IP over some lower level physical layer, not some custom content stuffed into an IP packet :)

(It's absolutely worth reading some of those old April Fools' RFCs, by the way [0]. I'm a big fan of RFC 7168, which introduced HTTP response code 418 "I'm a teapot".)

[0]: https://en.wikipedia.org/wiki/April_Fools%27_Day_Request_for...

That's layer below - using air+pigeon as your PHY and paper as your MAC