Artist here. Personally I wouldn't go straight in with pens unless she's specifically asked for them.
Pens are appealing and colourful, but they are actually tricky to use because they are permanent and unforgiving. It is hard to learn to draw with pens and it can be off putting if you make mistakes.
If she wants to get better at drawing, get her some decent sketching pencils (e.g. Derwent or Faber Castell) and an A5 wire-bound sketchbook (cartridge paper) that she can take out and about, and just start looking and drawing the world around her.
Also good to have is a set of pan watercolours (tubes are messy), a couple of decent brushes, some water-soluble coloured pencils , and a watercolour/ mixed media sketchbook or pad.
Derwent is a good brand for all of this stuff except the watercolours - for those I would recommend Cotman/ Windsor and Newton.
Don't be tempted to buy huge sets of paints/brushes that are cheaper - get one or two good quality things.
I recommend Jacksons art supplies online for good quality stuff, you won't tend to get great quality at places like The Range and The Works. Hobbycraft is OK.
Depends how serious she is about it though because the cheap stuff has its place for kids who just want to blaze through a lot of colours. But if she wants to really learn to draw/ paint, I recommend the above.