Oops I think it depends on the birthmark really - I know that's not much use to you. But a lot of them do fade away completely.
For e.g. a friend of mine had a baby with a strawberry mark on the hairline / forehead and it was quite raised and noticeable (and warm and soft and a rather lovely part of him actually) which gradually faded and by about 4 or 5 had shrunk away to nothing of its own accord.
On the other hand, ds1 had quite a raised and textured one on the back of his neck, quite thick really, and he has had 3 operations to take it off in sections - not laser, which would be easier I imagine as ds1's ops involve stitches etc afterwards, no fun. He still has 1 section left.
If it were me I think I would take her to a dermatologist - not to start laser treatment in a big rush, but to get her under consultant care from the off - the dermatologist can photograph it and make whatever detailed dermy notes they make, and monitor its progress. That way if you do get alarmed you won't get stuck choosing a dermatologist / going on someone's waiting list (if Eng is in any way like here in that regard).
That's what we did with ds1 - because his was a bit thicker than normal they took a biopsy of it to check all was ok; and when he was old enough, and it hadn't started shrinking or fading, the dermatologist spoke to us about what the risks were (e.g. as it was the back of his neck, we were always concerned about exposure to the sun, etc, he lived in one of those Foreign Legion hats every summer) and when we and she felt he was old enough, she started a series of small ops, giving each section time to heal and doing another bit the next year.
It may be a bit alarming to you to think about dd2 having laser treatment etc, she is still such a small scrap - so I would focus on the likelihood that it will fade, but have a dermatologist lined up, informed & on your team on the offchance it doesn't and you want someone topnotch to be in charge of things.
I don't know what you others think?