She could use the pots of La Riche Directions. They wash out (and they're very good in terms of hair condition and colouring).
HOWEVER, she must not, under any circumstances, use a permanent colour over the top. A lot of vegetable based dyes (definitely the blues and blacks, as they contain blue, never mind Henna of all kinds) contain compounds that, when mixed with those in a permanent colourant, start an exothermic reaction. The hair melts.
I've had black (blue, red, purple, white blonde, turquoise....) hair. When I was considering a different colour at the salon for a change, the hairdresser offered to do a strand test for me - he phoned the next day and said I needed to see this. I watched a second strand of hair melt.
To use the pots, get at least two (they're cheaper from shops that specialise in Ethnic beauty products rather than online or from your friendly neighbourhood Alt. Shop). Get some very dark towels (it will wash out, but why worry about it. She needs to wear a black t-shirt (as if that's going to be difficult for her). And gloves. Lots of gloves.
Put it in from the under side/back of the neck first and work it in well. Some people use a carrier bag to protect the house from any drips. Leave it in, then rinse and rinse and rinse and rinse and rinse.
The splashes all over the bath will come off easily. Any in dryish grouting will come out with bleach.
She'll probably need a dark pillowcase and it will come out with every wash. But it won't hurt her hair.
I adore baby Goths. They are just the cutest.
(There will also be dark red/black/blue/purple lipstick, lots of black eyeliner, assorted bracelets, shoes, most likely stripey socks and silver jewellery. But check what they're actually calling themselves. Nothing irritates a Baby Goth more than being told they're a Goth or Emo or Alt Rock or Greaser or whatever you have said if they're actually a Scene Girl/whatever it is called now. but I still call them Baby Goths in my head)