We went through this waiting for the 10.2 update last year.  Verizon was the last carrier on the planet to provide that update.  It is possible 10.3.1 may be available in 6 to 8 months, but given Verizon's track record, I wouldn't count on it.  By the time (if) they make the 10.3.1 update available, 10.4 will be out, and again, Verizon will be way behind the curve.  This is all too typical for Verizon.  Their support for Blackberry has been almost non-existent.