It is a difficult one.
I say this as a teacher and as a self harmer. I have recently been inpatient because of my self harm and I am currently actively self harming. I have third degree burns all up my arm and I am struggling to walk from the cuts on my legs so my self harm is quite public at the moment.
I think you can absolutely be a teacher or work with children if you self harm, the two are not mutually exclusive. I am not currently working but I have been (and am?) seriously unwell at the moment and unfortunately that is just not compatible with being a teacher. It is barely compatible with living.
I think she is ill-advised having recent injuries that can be seen, it does raise uncomfortable questions from colleagues, parents and children and I think for the sake of an easy life covering up at work is preferable. I appreciate that people should not be prejudiced or influenced by self harm but it is a scary thing, it is quite difficult for many people to process.
I would not say anything to her, I don't think it is your place to, although I can understand your concern. I have been asked about my arms by children (I wear 3/4 sleeves and until my recent ridiculousness 
my wrists were clear of scars) and I have skirted over it. I have never discussed it with parents and for parents evenings I would usually wear full sleeves and if asked I would not comment on it. I was pretty open about it with colleagues because I found it gave me some ownership of it, and once you say "I used to self harm" people really have nowhere to go with it :) I suspect her colleagues may know about her current SI.
I would also advise against going to her manager - people can be funny about SI and you don't want to be the one to put her in a difficult position. Especially if your concern is read wrongly and the manage interprets your concern as a complaint.
It is enormously hard walking round with a big sign pointing to your mental illness. I feel like people look at me and know, every time it takes me a few minutes to get up, every time I wince in pain from someone catching my legs, every time I roll up my sleeves and people see my dressings and scabby burns. It is hard, but there is a lot of value in still being able to function and live while you SI and good for her for managing. If you want to support her, give her a lovely card and flowers from your DD for being a fantastic nursery worker - things like that really do make a huge difference.
And actually actively self harming and working can be difficult. I spend much of my life very uncomfortable due to various stitches holding me together, I am not sure how well I could physically function at work. I hope this is not the case for her, but if I had a child in nursery and I saw recent SI on their carer I would be concerned about infection risks and the impact the injury would have on the carer's movements.
Oh and finally - people can be in treatment and still be self harming, sometimes self harm is the last thing to go. It is accepted as a (not very good) coping mechanism in mental health and work is often done around harm reduction prior to work being done around stopping it. I see someone three times a week and I still self harm, they can't actually stop you, they can just support you to come to a place where you don't need to or where you can use alternative strategies.
This is really long :) I just wanted to give my own perspective.