Well first off let's be realistic about Kingston's defenders. Only 600 are regulars and the rest are militia of dubious quality. Not only is the US force 3x larger but there's a much higher proportion of regulars there to boot
Well remember, these same militia handed the Americans their heads at Chateauguay, Crysler's Farm, Queenston Heights and Lundy's Lane to name the most famous. The militia formed the backbone of most of these battles, and the regulars in 1813 were definitely not comparable to their European counterparts.
That's in the open field. Against entrenchments the contest isn't likely to be fair.
You do raise a good point about Dearborn. My preferred POD would be him dying in January 1813 and Pike taking over. Under Pike camp conditions are improved as is discipline, thus in 1813 you have a much stronger American fleet/army attacking Kingston. I think that's quite doable.
Killing Dearborn is a great start. The conditions of the American army and the overall efficiency would sky rocket most likely. The only remaining problem would be Chauncey and whether he would risk decisive battle or hold back a bit, which could make or break the land battle.