You would be surprised at how many people buy a small tractor with pond digging in mind.
You can do it, but it's a monumental project, and you must be patient. Don't dig with a FEL. Use a disk harrow and break up the soil 3" 4" deep at a time. Scoop it with the FEL, and load it on dump trucks or trailers, and make piles just outside the pond to give away or spread later. A small tractor can dig a pond really fast that way. However, the real problem is not in the digging. My little tractor with a 6' disk harrow could keep a dozen big loaders and dump trucks busy. The Devil is in the hauling!
I'm 1/2 finished with a 150'x400'x6' average depth pond. It's been a real adventure. I've gotten some help from neighbors, who bring their tractors, trucks, trailers, and wheelbarrows to get the free dirt. In the end, you can only count on yourself.
The first 2 feet are murder, because nearly half of the digging is in it. As the pond grows deep and slopes to the center, each successive foot of depth consists of a lot less digging and hauling than the previous foot. Don't dig 2 feet and give up! Unless you hit hard clay or rocks, you are half way there at 2' or a little more.
All that said, if you can afford it and are in a hurry, hire it out!