Is it possible to have dual internal hard drives in a 2009 mac mini? I want to have an SSD for the OS, and the existing disk that came with the unit.

Is this possible?
There are three possible models of Mac mini that came out in 2009: Early 2009, Late 2009, and the Late 2009 server variant. 

The server variant comes with two hard drives already (and no optical drive), so I'm assuming you don't have that one. However, since the server and non-server variants use the same case, it seems a safe assumption that you could fit a hard drive in the space usually taken by the optical drive. Getting the hard drive to be held properly in that spot might be difficult, but maybe one of the optical drive replacement caddies could help.

There doesn't seem (and I don't remember there being) a significant physical difference between the early and late 2009 models, so I think the same assumption would apply.

In any case, be sure to check the iFixit (or similar) teardown before you start and do tell us if it works (or if it doesn't)!