Cross-Platform Windows plus Mac

I'm a C++/Windows developer at a small (well, tiny) company, and I've been
asked to explore what it would take to create an application that could be
built for both Windows (XP + Vista) and Mac.

I've never done any Mac programming, so I was hoping people could send me
suggestions for books, web sites, tools, etc. that talk about ways to
accomplish this.  The application has no UI except for an icon that lives
in
the system tray on Windows (which would be the ... what? ... on Mac), so
that makes things easier.  I'm imagining 3 approaches ...
1) Have two totally separate codebases, one for Windows, one for Mac.
2) Have some code be Windows and Mac specific, and then the core
functionality be shared code.
3) Buy a product like QT

Management has said that if QT is worth it, they'll spring for it, but I
don't know enough about it to know if (QT + my learning curve on QT) < (my
learning curve on Mac + time to sup****t multiple code bases).

Thanks!
Chris