I have not given Pimpiowyn a weapon because she is a young half-hobbit (in her tweens) whose favorite pastimes are eating, eating, and (for variety) eating. In her sheltered life at the Elven Farm, she has not had use for weaponry.
Since it is imperitive to such a dangerous mission that she have something to at least protect herself, she can be given a sword at a future time. I'm thinking there are three possiblities, 1) Lord Roneld gives her one before they depart 2) Kuruharan sells her one 3) she finds one a la Bilbo and Sting.
I'm not paticularily leaning towards any one of those at the moment.