I believe that the Act for Establishing Religious Freedom was passed by the Virginia General Assembly on January 16, 1786. Did the Governor of Virginia at the time have the right to veto it?
No, the Governor of Virginia had no power of veto in 1786.
The Commonwealth of Virginia adopted its first Constitution on 29 June 1776. This was superseded by the second constitution in 1830. The First Constitution is therefore the one that would have applied in 1786.
That Constitution did not give the Governor any power of veto. It states simply that:
All laws shall originate in the House of Delegates, to be approved of or rejected by the Senate, or to be- amended, with consent of the House of Delegates; except money-bills, which in no instance shall be altered by the Senate, but wholly approved or rejected.
The power of veto for the Governor wasn't introduced until the 1870 Constitution of the Commonwealth of Virginia, following the constitutional convention of 1867-68. In Article IV of that constitution we see the following:
Sec. 8. Every bill which shall have passed the senate and house of delegates, and every resolution requiring the assent of both branches of the general assembly, shall, before it becomes a law, be presented to the governor; if he approve, he shall sign it; but if not, he shall return it with his objections to the house in which it shall have originated ...
which gave the Governor the power of veto over laws from the assembly for the first time.
A useful source for the subject is A History of Virginia Conventions by Jacob Neff Brenaman.