Last summer I planted a Hale Haven peach tree (over a spot where a compost pile that had "cooked" for 2 years).  The tree came in a 5-7 gallon container from a big box store.  

Then, early last winter, the neighborhood rabbits chewed on the lower bark.  I was afraid the tree would not grow, but it has grown a lot during the spring.  Yesterday, June 20th, to my surprise I discovered there are 3 little peaches growing, which are the size (and firmness) of golf balls.  I also discovered, much to my dismay,  what appears to be canker, (according to my neighbor).

FYI, About 10 feet away from this tree are three, dying nine-barks.  They are covered in a white powder.  Fungus?  This isn't a separate question, but perhaps related to the issue of the peach tree.

I have read that the canker infects the whole tree, because it is inside the root system; and I have seen advice to cut the affected branch(s) off.   (Does that even make sense, since the whole three is infected?) 

Because the split, infected area of my tree is at the top of it's trunk, just before the branches start branching out, I think it is best to cut the tree down (and plant another type of tree).  However, no where have I read to cut a tree down.  Your opinion is welcomed!