Does a dietitian teach?
Not necessarily, but there's no rule to say they can't, and they would hopefully be better at teaching about diet than other people.
And that is what the clause "A consulting dietitian by profession" adds to the sentence; it informs the next clause by stating something about the fact that she was teaching about healthy eating.
Is the use of the noun, 'teaching' correct there?
Well, more strictly it's a gerund, and it's necessary because in using a transitive sense of the verb to enjoy here we need a word that can act as a noun to be it's object. Compare with the incorrect:
*Tina has enjoyed teach young children…
*Tina has enjoyed taught young children…
These don't work precisely because we don't have an object that is a noun or a form that can act as a noun, as a gerund can.
And can the use of the present perfect form of the verb be justified?
Assuming that what it says is what is intended, then yes.
One of its uses is to state that something has happened over a period from some point in the past up until the present or very close to the present.
Combined with the following "…for over a decade", this tells us that at some point over a decade ago, she started teaching children about healthy eating habits, and enjoyed it, and has continued to do so up until the present day.