I'm trying to put this illustration onto the whiteboard (left) But when I try to shrink it, it gets all messed up. I tried doing path-outline stroke. It worked but I losst all the color that had already been filled.
Since this is more complex graphic, use Object > Expand... rather than 'Outline Stroke.' While these are pretty similar commands, the expand option is a bit more in depth, handling strokes, fills, gradients (if applicable) and will maintain the proportions of your original artwork while resizing:
For a nice summary on 'Outline Stroke' vs. 'Expand' (and when to use each),
check out Cai's answer on this question.