The problem is most likely with QAuthenticator, but can be seen as follows:

Launch the Qt demo browser
Configure proxy settings to point at a squid proxy that uses "ntlm_auth"
Open url "http://qt.nokia.com" – it works!
Open url "https://qt.nokia.com" – it hangs and never displays the webpage.

Squid log reports: "got NTLMSSP command 3, expected 1"

I am inclined to believe this is a problem with Qt, because Firefox works fine with the same setup.

Squid is configured as follows:
auth_param ntlm program /usr/bin/ntlm_auth --help-protocol=squid-2.5-ntlmssp
auth_param ntlm children 5
acl ntlm_users proxy_auth REQUIRED
http_access allow ntlm_users

Squid is built as follows (Mac OS X 10.6):
configure --enable-ssl --enable-delay-pools --enable-auth="basic ntlm" --enable-basic-auth-helpers=NCSA --enable-external-acl-helpers=unix_group --disable-ipv6
make
sudo make install

(There is one file permissions problem, which I worked-around by giving everyone all access to /private/var/samba/winbindd_privileged and the "pipe" inside of there. That's not the way you're supposed to do it, but that's irrelevant for this bug.)