Did you see:

  --output-type
    can be "base16" or "raw". "base16" is human-readable, and "raw" is useful
    if you want to pass the output to another program like a bar code or
    QR code generator (though note that scannable codes have some of the
    disadvantages discussed above).

It is as easy as:

  paperkey --secret-key secret-key.gpg --output-type raw | qrencode -o qr-paperkey.png

If you are curious David Shaw is one of the main GPG developers.

If you are going that route anyway, you can just use optar[1] and just print the whole encrypted file.

[1] http://ronja.twibright.com/optar/

Just generate a QR code from the output ("programs should do one thing and do it well")

Just add qrencode[1] to the mix:

> gpg --export-secret-key my-key | paperkey | qrencode

[1]: https://github.com/fukuchi/libqrencode

I went with Data Matrix to backup my (encrypted) PGP key pair to paper. When I compared QR and Data Matrix, Data Matrix "won" because of its ability to encode pretty massive amounts of data by chaining individual barcodes together. (QR tops out at around 3000 bytes; less if you increase the error correction level.)

That said, I'm not sure if I'd make the same decision today. QR code readers are plentiful, and Data Matrix readers are comparatively rare.