Note that people ship (themselves, implicitly) quite readily.
At the very least, your future Sailor will make a trip to MEPS for initial processing, then a second trip to MEPS for final processing on the day s/he ships out to basic training. -- Navy For Moms
And, yes, inanimate objects can "ship" meaning to begin their journey. Of course, being inanimate, they don't actually do anything. A person begins that order's journey; that order has had its journey begun; but we can say it began its journey. Similarly, it has been shipped, but we can say it shipped.