Edited: the examples of pegging coke cans at 75 meters are all reasonable,
Not to put too fine a point on it - but that would be amost impossible. Hell even wth my glasses on I'd barely even see a coke can at 75 METRES. 75 feet - would me more realistic. and I suspect that's just a misprint.
so my pennyworth:
1) you would need to qualify the practice. If you want her to be extremely good she would need to practice for an hour a day - minimum. However if you make the slinging part of a therapeitic or meditative process, it would fit quite nicely.
slinging practice is very repetitive, also a good general body workput - so would fit as part of her daily routine.
She would also need to have a particular affinity for the sling. Some do some don't. As wit everything else in life there are always going to be those who are just better at some things than others. So given those conditions she could realistically be very very good indeed
2) leather armour usually only covers the torso and part of the head. this leaves arms and legs as much better targets than either the torso or the head.
A tremendous amount will depend on her ammunition. If she uses cast lead bullets or glandes, then she could be very dangerous out to about 200-250 yards. If she's just using picked rocks, you'd have to knock that down to 150 yards maximum.
Bear in mind that small darts can also be used from a sling. And wth medical knowlege they could be poison tipped - which would increase her deadliness 10 fold. A well slung dart will penetrate leather armour and a fast actin poison would make each hit a kill.
Even without poison a barb ended dart will leave a bloody and potentially debilitating wound.
It would also be a good idea to equip her with a hoopack - combined staff, utility stick and staffsling.
This could also be her close quarters combat weapon as well as a tool for delivering heavier missiles in battle or other circumstances.
A properly used quarterstaff - with the exception of a projectile weapon - is the most effective close quarters weapon there is. Not necessarily as lethal as a sword, but much more practical and effective.
Again you would need to make practice part of her daily routine.
It can't be stated too frequently or too firmly that proficiency with ANY weapon can only come with long practice and familiarity.
3) never heard of them - who wrote them ?
If the sling is going to feature to any great extent then your heroine must belong to a tribe that uses slings extensively. Otherwise it's unlikely she'd ever take one up.
On our plane of existence - for example - she'd have to be a balearic islander or member of another moniroty group known to use slings. Obviously the further back in history you go the more you'll have to choose from.
She would also most likely carry 2-3 slings or different length and - possibly - design.
A short sling -12-18 inches is short enough to be effective indoors and in confined quarters, as well as being effective to 100 yards.
A medium length sling always close to hand for general usage and a longer sling for distance bombardment. The advantage of the hoopack is that it is very easy to fit or change the sling attached to the forked head. So as long as she uses a sliding finger loop and a small fixed loop instead of a release knot, each sling could also be attached to or removed from the hoopack in very short order.
IN case you were wondering, yes I've given some considerable thought to writing slingers into fiction - so all I'm going to tell you is the basic stuff