Which English word for describing this little girl's hair thing?

Yes, pig-tail is probably the most accurate term. (If all of her hair was gathered up it would be a pony-tail). You would have to specify where you want the pig-tail, on top of the head, side, etc. Many young people have two pig-tails if there is enough hair, one on either side of the head or on each side of the back of the head. Very cute.