[@MonsieurShade]The fort has a shortage of food right now, so they wouldn't want to let you bring it with you.  They don't even have horses at the moment, though once some trade has happened it may be possible, as the natives could sell them food for more valuable trade goods the Empire could ship in.
I was actually thinking of being a Shaman at first, but I thought it would be more realistic for them to have a food shortage (many settlements in the early American colonies had food shortages) than to have animals, so I figured that would fit the situation better.