I suspect the reason they are not available, is that a puddle jumper isn't really safe for a 1 year old; it doesn't orient their heads up automatically, like a Type I lifejacket will (which is what is recommended for a 1 year old). I'd worry that even in a pool a 1 year old would too easily orient face down in a puddle jumper, particularly with the lack of arm and upper body control.
There are some perhaps less frustrating suits out there; while most of the infant suits are going to be Type I and thus have the big neck piece (which is usually what is frustrating), there are also "float suits" and such, many of which have removable flotation pieces (so they are combo bathing suits + flotation devices). You may want to go to an REI or similar that has a large selection and just see what is the least irritating to your tot.
My wife also suggested that at 1 years old, it might be as much or more fun just to be in a regular bathing suit and in your arms. That's mostly how we play with our one year old, anyway; and it's not like you would really be able to be much further away anyhow (particularly with a one year old, it wouldn't be safe for him/her to be more than a foot or so away). I don't know if your one year old has as much body fat as mine does at 27 pounds, but he floats somewhat by himself anyway, which makes it easy to play with him in the water.