Just another opinion here
Firstly, at least you just asked advice rather than just doing it completely uninformed. 
I would reccomend going to a doctor ( pediatric ) and taking as much relevant information as you can: Documentation / photos and your old implant syringe(s) if you have them.
Take your Kiddo along with you so it can all be explained, 10 year olds are not stupid, but they do need guidance and direction with their decision making, she will understand and would appreciate being included, since it is her decision at the end of the day.
Show the doctor yours, and how it lays under your skin and get the professional medical advice from them.
Explain to the doctor about possible migration issues some people have had, and also take some info about how they can be removed if required.
From a personal standpoint, I would follow my advice above, dont rush into it, let her think on it, would the alternatives suit her ( Wrist bands, nail stickers, key fobs, necklace etc)
If she has had time to think, seen the size of the needle, spoken with the doctor, given alternatives, I would say you had done your due dilligence as a parent, and it is informed consent ( albeit, a 10 year old ) then I would go for it ( I am happy with my knowledge around the implants and their safety, and would rely on the doctor for their knowledge around my child, plus my own due dilligence ie. Medical research), who knows, she may back out before it happens.
Kids do far worse things with more severe risks everyday, many unsupervised and without consent.
As mentioned above, kids get their ears pierced which is arguably more risky, young boys are mutilated/assulted every day when they are circumcised without consent and at far more risk than an xSeries install.
I think your next and biggest hurdle is finding somebody who would be willing to do it; You could ask the same pediatric doctor ( Unlikely, but worth a try and at least it will be somebody with medical training and familiarity with childrens anatomy…that sounds dodgy, but you get what I mean ), If the doctor says no, take the same information to some piercers, and as you are in Russia, you may have more open minded people than some other countries.
Some reference material to get you started
Here is a VERY informative FAQ about x-Series implants, some of which is covered below. But it is recommend you read these FAQs.
A doctor, nurse or medic would be able to but they will likely take more convincing…
Watch Installation procedure Guide 1
Watch Installation Procedure Guide 2
Watch Needle insertion angle
How to approach a professional DT Info
Whatever you decide, let us know how it goes.
I would also suggest keeping an eye on it periodically, at least until after puberty / growth