I know how you feel; my boy, now 4, went in for the first time at about 14 months and it was depressing and scary for everyone except him; he had a pretty good time running amok in the halls and playrooms despite trailing his picc line. Getting IV meds via a picc line is infinitely better than through a normal IV needle.
As for getting the picc line placed, your child will be sedated so that procedure is not going to be all that troubling to her. Scheduling is important since they'll probably say she cannot have anything by mouth after midnight the night before the picc is to be inserted....you should push for the earliest slot available so you're not also having to deal with a hungry child while you sit around nervously waiting.
She'll most likely get an IV placed first and that's where all my boy's big grief has come from...we've learned to insist that they call up the best "sticker" on staff because the real experts make it go smoothly and on the first try but those less adept can cause alot of fear and pain for the patient. There are numbing creams (Emla is one) that you can ask for to reduce the needle pain. Also, if you google "picc line" you'll find some very complete explanations and pictures of the whole thing.