My Dad's mom (my grandmother) is 4'11. My dad and my uncles are all 6'3 and above, and my aunts are 5'11-6'1.
My mum's family is Norweigan & Scottish and all QUITE tall... but it's my Dad's mum being so little that is more to the point. A little mom can have TALL children.
On BOTH sides of my family this is the growth pattern:
CHUB up, and SHOOT up. We're all fully grown (height wise) by age 11-13. Which means 6 foot +. We get rolly polly FAT, and then in a month you can see our ribcage, spine, hipsockets. We grow FAST and we grow YOUNG.
My own son ate apx 20oz of breastmilk or formula PER FEEDING, and followed the exact same pattern. 10lbs & 23 inches at birth... over 25lbs and a good several inches longer/taller by 6mo. 37.5" by 2yo. He's growing slower than I did (I was 5'2 by age 8, he was only 4'9).
ALL of us fast growers ate a TON, and grew up "perfect". The only thing fast growers really need to look out for is not screwing up their joints by running/high impact sports during growth spurts. You'll know, because they will say those joints HURT. If her joints hurt her, tone things down a little bit until the growth spurt passes.