Completely normal.
It´s not only normal, it´s also good that it ate it, because it´s a way of getting back some nourishment from it.
The rate at which they shed varies a lot. Juveniles can shed very often, once a week or even more. Adults tend to shed much less frequently. Also, ill or injured individuals sometimes shed very often.
Adittionally, a newt will automatically shed when it changes from being terrestrial to aquatic, and vice versa.