No, there will not be any problems. VFS Doha will send the documents to the Canadian embassy in Abu Dhabi. As Saajye pointed out, the Canadian Visa Officers will be dealing with your application and that has no connection to UAE/Qatar diplomatic ties whatsoever. The only thing may be that when you send your documents, they will possibly go through Iran or Oman, adding to the cost of transmitting it. But if you send it through VFS Doha, they will be dealing with it so everything remains normal.
And if you are planning to apply for September do it right away, since Abu Dhabi's Canadian Embassy is famous for its slow service. Good Luck.