Wow, where's the other half of the tree ??

Okay, I know nothing about peaches, though that's a pretty drastic pruning job.

It will be fine.

I once ordered a Stanley prune plum bare-root from a mail order place. It arrived looking just like your peach. I had to wonder if they ran a whole bundle thru a band saw to shorten them enough to fit a smaller shipping box? I was very concerned. I planted my "broomstick" of a plum and it budded out late June and did just fine. Went on to become a beautiful tree.

Since your peach is a Prunus too it should do the same.

While many people are turned off by that trunk, it's actually a great way to get the tree growing the way you want it. It will bud out and you can pick and choose which branches you want to be your main scaffolds. Dave Wilson pushes a type of pruning used in backyard orchard culture. One that starts the branches closer to the ground and the finished height of the tree will be closer to what you can reach with your hands. I would plant that tree and prune it off at the height of my knee. If you want a bigger more full size tree, just let it grow taller.

That is pretty standard practice for mail order bare-root trees. Most of the research i have done actually recommends that when you plant bare-root trees, to prune them down to waist high (or about 3ft tall). That feels a bit excessive to me, so when i get something like you have, i leave it be. As long as it came from a reputable nursery (Dave Wilson is and excellent nursery, especially for people on the west coast) there is no need to worry. If it is a DW tree from a third party nursery (that is how i got mine) you should make sure to have a 1 year warranty on the tree, just to protect yourself.