Are there any quantum computing-secure open key exchange algorithms already implemented in SSL/TLS which I could use on my web server?
The TLS specification allows negiotiating any encryption method to use between the client and the server, so in theory TLS can be used with quantum safe algorithms. Unfortunately, the standard implementations (openssl) currently don't support such algorithms.
There are some projects that aim to change this, such as Open Quantum Safe:
We've integrated liboqs into a fork of OpenSSL v1.0.2 to provide prototype post-quantum key exchange ciphersuites in the TLS protocol. Researchers looking to try additional post-quantum algorithms can easily add more algorithms that follow the OQS API. You can use our modified OpenSSL to prototype quantum-resistant cryptography in Apache httpd or other applications that rely on OpenSSL. The goal of this integration is to provide easy prototyping of quantum-resistant cryptography and should not be considered "production quality".
So it is currently technically possible to provide quantum safe crypto, but it is still experimental.
As far as I know all the available-options like RSA, DH, elliptic curves etc are insecure to quantum computer brute-force.
All the currently used asymmetric algorithms (RSA, ECC, DH) can be broken by a quantum computer. There isn't really any "brute-force" involved either. I wrote a blog post about how this works.
are there any activities by major industry players to allow QC-secure algorithms in the near future?