To keep you at ease, I could not find any carbon dating of the GoB.
But there is enough evidence to conclusively say…it is a fake, as well as the secret bible:
quora.com/What-is-the-truth-about-the-1500-year-old-Bible
The author: not Barnabas
The author of the Gospel of Barnabas could not have been the biblical Barnabas. The real Barnabas was a generous encourager of the early church (Acts 4:36-37). He was not one of the original twelve disciples of Jesus as the Gospel of Barnabas mistakenly claims. Barnabas was the one who persuaded the apostles that Paul had changed from a persecutor of the church to a follower of Jesus (Acts 9:27). The true Barnabas was a missionary, telling the good news of Jesus (Acts 13:2).
Date of authorship: the Middle Ages
If the Gospel of Barnabas were written in the first century, it would have been quoted in other documents of the same time period. It is not cited, however, a single time in works of either the church fathers or Muslim clerics until the fifteenth century. Those who claim the early authorship of the Gospel of Barnabas may be referring to the Epistle of Barnabas—a first-century book, though not divinely inspired.
A reading of the Gospel of Barnabas clearly shows that it was written neither in Jesus’ time nor shortly thereafter, as alleged. It contains far too many historical errors. The Gospel of Barnabas contains quotations from Dante Alighieri, references to an edict from Pope Boniface, and descriptions of feudalism. Therefore, scholars place the date of authorship around the fifteenth century.
Legitimacy: full of errors
The descriptions of Palestine show that the author of the Gospel of Barnabas was not familiar with its geography. He alleged that Jesus sailed to Nazareth—an inland city.
The Gospel of Barnabas says that Jesus was born when Pilate was governor, but history records Pilate becoming governor in A.D. 26 or 27—long after Jesus’ birth.
Trustworthy scholars have exposed the Gospel of Barnabas as a counterfeit. Therefore, it cannot be trusted as the biography of Jesus’ life.
y-jesus.com/more/gbs-the-gospel-of-barnabas-secret-bible/4/
Christian writers such as Irenaeus wrote extensively about anti-Christian documents such as the Gnostic gospels, classifying them as heretical. Yet, not one of Ireneaus’ letters or documents mentions the Gospel of Barnabas. There is simply no mention of it from any early writer.
Perhaps most indicative of its late date is that the Gospel of Barnabas describes medieval life in Western Europe, as well as a 100-year Jubilee, which wasn’t declared until the fourteenth century. How would Barnabas or any first-century writer know such historical detail hundreds of years before it was declared?