Last I did this hike was in August 2003, on a traverse from Adirondack Loj to Upper Works. I recall two ladders on the trail itself and a short ladder leading up to Summit Rock.
In my direction of travel (i.e., descending from the Pass toward Upper Works), the first of these on the trail proper was a single, vertical ladder with 11 rungs. The second was in two sections of 7 rungs each, with the first section pitched at about 60° - 75° and the second section vertical.
I'll let you make a judgement as to whether this is doable with your dog.
G.