Can I boat from Lake Champlain vermont to quebec city?

It looks entirely possible. On checking the route with "Google Earth"
, there is a substantial waterway/river system leading from Lake
Champlain north, passing St. Jean Sur Richelieu/ Iberville, then
Beloeil, and coming out into the St. Lawrence waterway at Sorel. From
there it is northeast tp Quebec. What Google Earth does not shoe is
the depth of water and possible rapids, if any. As I am situated on
the west coast of Australia, where the whole state has only a few
rivers with most of them dry unless it rains, you are very lucky. Not
with the snow, though.

From this site it would seem so:
http://www.pilothousecharts.com/Hudson.htm