Yes, that is Peach Leaf Curl.
There is no control once the leaves have come out. The best you can do is to properly fertilize and deep soak the tree so it will be as strong as possible.
Ask at reputable places for the optimum timing in your area for spraying.
Around here (quite different from NY) we spray several times through the dormant season, and use lime sulfer (fungicide) and combine it with horticultural grade oil, like Volck oil or similar. The oil smothers a lot of overwintering insects.
Peach trees can be any size. Dwarfs stay smaller with less pruning. If you want yours to be that small do not do all the pruning in one year. Selectively remove just a few too-tall branches each year over a 5-year plan. Gradually you will work it into a smaller scale.
Some fruit tree diseases are more active at certain times of the year, and the plant is better able to fight certain diseases at certain times of the year. Ask that same reputable place about the optimum pruning time for peaches, and if any protection is needed if you cut large branches. Perhaps nothing is needed, it is better to let the UV from the sun sterilize the cut. In some trees a large cut would attract insect pests. Best to know ahead of time, and be prepared.
Ways to find local experts:
Department of Agriculture.
Extension offices.
Master Gardener program.
Certified Nursery People.
Certified Arborist.
There is so much info on line, too, I'll bet you could research and get all the answers, too!
