TLDR; An experimental version of GnuPG for post-quantum cryptography does exist, CodeCrypt. As for SSL/TLS, implementation is possible but getting servers to use it would be a nightmare. For true, absolute security, use One Time Pads.
Long Version: Well, it's 2020 now, and the only solution that looks decent is CodeCrypt (mirror of repo hosted on a site that takes ages to load). It's hardly a complete answer to your question, but it's something. It's designed to work like GnuPG, as the README begins:
This is a GnuPG-like unix program for encryption and signing that uses only quantum-computer-resistant algorithms:
McEliece cryptosystem (compact QC-MDPC variant) for encryption
Hash-based Merkle tree algorithm (FMTSeq variant) for digital signatures
You requested the McEliece algorithm, and I think this is probably the best you'll get as of right now. In terms of security, I haven't reviewed the code myself, but it's recommended by Whonix (leading open-source anonymity software used and recommended by Snowden himself) in their page on post-quantum cryptography. Those are pretty good credentials, and certainly enough to warrant interest and research in the project.
In terms of convenient encrypted email with it, unfortunately, the only extension for Thunderbird I could find is "an experiment", AnnealMail, so I wouldn't recommend using it in any serious scenario.
CodeCrypt itself is apparently an experiment, but its recommendation by Whonix and Whonix's guides on its use are promising. It's certainly worth trying out, and given that I wasn't able to find any other GPG-like systems that implement PQCrypto, I'd say it's a viable alternative to GPG for now. Probably, the best solution would be to double-encrypt, once with GPG (which we can presume to be not backdoored), and then once with CodeCrypt (which we can leverage the possible security of without trusting the system to protect from backdooring). This gives us a solution secure against classical attacks at least, and allows us to leverage the possible security of CodeCrypt, without completely trusting it yet, given that it is very new.
As for SSL (by which I sincerely hope you mean TLS), good luck with that. Given the existence of CodeCrypt, the protocols shouldn't be too difficult now, but getting them to work with servers other than your own? Good luck. It'll be like IPv6, a great solution to a very real problem, one that still isn't globally implemented, and has been being phased into for years. Replacing TLS would be hellish, because not only would you have to have a custom browser (or at least a custom build), but you'd also need servers that support it, and a translation gateway from this protocol to TLS would be utterly security-wise useless, defeating the whole purpose. I think we have a while to wait yet before widespread use of a PQCrypto protocol that can stand in for TLS.
If you want PQCrypto that is absolutely guaranteed, and doesn't even need (and really shouldn't use) a computer, check out One Time Pads. The KGB used them, and they're the only information-theoretically secure encryption algorithm we have (to my knowledge). That means that even an adversary with literally infinite computational power couldn't break it. You want encrypted email that's really perfectly secure? Use them. Be warned, say goodbye to the instant in instant messaging if you do!