Asalamu 3alykum
Just to add to brother Dusters comments the Quran did not teach or invent a new calendar.
It had spoke to the recipients with the calender they already had. This is obvious by that it mentions a name of a month of Ramadan or the day of Jum3a for example.
It is also possible that there may of been various calenders and ways to tell time that was in circulation during the Qurans was being revealed and before it. There seems to be evidence from 18:25 that not all people shared the same calender. Some said 300 years some said 309 years. A calender is neither correct or wrong. Its just how people choose to agree on how to communicate time and a relative point of view to communicate time.
However God did choose to pick the system of the Arabs to communicate His message and to point out when is the four sacred months and when people need to fast and congregate for prayers etc.
I don't see any reason to reject the tradtional Arabic calender year. One would need to prove that the current Arabic calendar we have with us today was changed/corrupted if they don't accept it.
There is however evidence from the Quran when the holy sacred months are and they do not align with the tradtional view. I think this is a different matter and the Quran does indicate or point out the correct holy month that God has choosen for His servants.
Please see article below and from 9:2-5 one may tell which month are sacred.
At the end we do need to understand that the Quran is for all people but need to carefully also understand that God had choosen to use the Arabic calender/language as a relative starting point of explaining His revelation.
Although God could of used any peoples system to guide people there does after all need to be a platform from where telling time, explanations and guidance needs to start off with and God had choosen the Arabic language to reveal His final Scripture and used that nations system to explain to humanity what He wanted. That being said it does not restrict guidance in Arabic only or only the Arabs. God guides whom He wills in whatever way He wills and when He wants.
Hope that also helps Insha'Allah
Salam
THE 'LOST' MONTHS OF HAJJ
http://quransmessage.com/articles/the lost months of hajj FM3.htm