While the Gospel of Barnabas does give an avenue of insight into the Islamic view of Jesus about the earliest date that could be ascribed to it, even without considering the mentions of Mohammed, is of the time of Mohammed because of other things mentioned in the text. There is no credible reason for anyone to take it as an authentic text written by Barnabas.
http://aina.org/news/2012022916569.htmHowever, beyond that, as the link points out above, the copy of the text in question is a pitiful forgery probably fabricated in the 21st century and certainly no earlier than the 19th, so it isn't even as old as the known authentic copies of that work.