Turner Syndrome would be XO- in other words, a missing X chromosome, not an extra one. So this baby does not have Turner Syndrome.
Since you know the baby is a girl and she has an extra chromosome on the 23rd pair, that means she is XXX, or triple X (also called superfemale).
http://ghr.nlm.nih.gov/condition=triplexsyndrome
What is triple X syndrome?
Triple X syndrome, also called trisomy X or 47,XXX, is characterized by the presence of one extra X chromosome in each of a female's cells.
Most often, this chromosomal change causes no unusual physical features or medical problems. Females with triple X syndrome are sometimes taller than average and have an increased risk of learning disabilities and delayed speech and language skills. Developmental delays and behavioral problems are also possible, but these characteristics vary widely among affected girls and women. Most females with triple X syndrome have normal sexual development and are able to conceive children.
How common is triple X syndrome?
This condition occurs in about 1 in 1,000 newborn girls. Five to 10 girls with triple X syndrome are born in the United States each day.
Triple X syndrome results from an extra copy of the X chromosome in each of a female's cells. As a result of the extra X chromosome, each cell has a total of 47 chromosomes (47,XXX) instead of 46. It remains uncertain why an extra copy of the X chromosome is associated with tall stature and learning problems in some girls and women.
Can triple X syndrome be inherited?
Trisomy X usually is not inherited, but occurs as a random event during the formation of reproductive cells (eggs and sperm). An error in cell division called nondisjunction can result in reproductive cells with an abnormal number of chromosomes.
Bolding is mine.