my niece does this all the time. I was on my way out once and she threw up all over me but as you say, missed herself!
Probably better that they miss themselves, babies aren't easy to get changed!
Thats really bad news! Sorry to hear it.
I there any way you could take it back? This happened to my Yaris, I phoned them, told then about the damage to my passanger door, they sent someone round the next day to sort it out.