Hi Brent, I'm glad that you like MoI's interface!

Yeah MoI itself does not have a fully automatic bitmap tracing function in it. Like Ed mentions WinTopo can do it, and there are several other possible choices as well, check out this thread for some more information:
http://moi3d.com/forum/index.php?webtag=MOI&msg=997.1

For your other question about extrusion - certainly MoI can extrude an outline like that, but the result of an extrusion will be a punched out slab with hard edges on it, kind of like when you take cookie dough and push a cookie cutter on to it to slice out a shape, there will be a flat top and vertical "walls" on the sides.

MoI doesn't really have a tool to make a bubbly or balloon-ish type completely rounded form from a complex outline like that, which is probably more what you want for a cartoon style model.

There is a technique that you can use described here:
http://moi3d.com/forum/index.php?webtag=MOI&msg=415.2
which can make a kind of blobby rounded shape, but you would have to use it kind of strategically on kind of more simple outlines, it would not at all be like a push one button of your 2D cartoon and automatically turn it into a rounded 3d cartoon.

As far as I know there does not exist any software that can do that kind of conversion in a fully automatic way.

You may want to try some other software for this that is more focused on making soft blobby balloon like cartoon shapes, here are a few possibilities:

http://www-ui.is.s.u-tokyo.ac.jp/~takeo/java/smoothteddy/index.html
http://www.archipelis.com/

- Michael