You don't have to have posts in the water.

Get some old car tires and attach them to each other with wire, so they are flat. You now have a flotation device.

Then build your dock, and attach it to the top of the floatation device..

Anchor the dock to the 2 land posts. Use chains leaving some play to accommodate the rise and fall of the water level in the lake.

This is the method used to build rafts. So you are building a raft, and using it as a dock, by anchoring it to the land.

If you are only going out 3' and the water is only 1' deep, you could always just wear boots. I would go out 6 feet, so there's plenty of room for me, my chair, my tackle box, my ice chest, and a friend.
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drain the lake! nah joke their are these things you use to put post in to support trees and things but i dont know there name! it comes over the post with two handles and you lift it and bang it down!
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If you don’t want to go the floating dock route, you have two options one is pounding in a post(s), the other is weighted. Since you are not at a deep depth you should be able to just pound in a post(s) to support your dock, you will want to check and see if you need permits/permission to install something like this and how deep it needs to be. The other way might be to use a concrete weight; they make concrete foundations for decks you can attach a post to one of those. Cheaper even than that is a five gallon bucket with a post and concrete in it. If you go the weighted route you might have to deal with shifting of the lake bed, but not if you go the pounded route, but you will need to get it in deep to have something sturdy.
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