Is this somehow possible? My development PC has VS 2005 and .NET Framework 2 on it. Can I install .NET Framework 1.1 and target a 1.1 framework environment using VS 2005 or do I have to install VS 2003 as well?

Directly no... Visual Studio 2005 is designed only to target 2.0 (and 3.0 later it seems)... not 1.0/1.1.

You are free to write code in 2005 and compile it externally for the 1.1 framework, you just need to limit yourself to using only classes and methods that are supported there.

One easier way to handle this is to use MSBee which is an addon for MSBuild and lets you target the 1.1 framework.