I typically get around $4 per dozen, but I also have some beautiful and colorful eggs. I once got... you better sit down for this... $16 for a dozen eggs. They were 11 duck eggs (which I have created a market for in my area) and 1 perfect goose egg. At the right time of year (Easter) I can get whatever I want for goose eggs. It's crazy!
I used to have a hard time moving duck eggs, but I love having ducks around, so I decided I needed to create a market for them. Irony of ironies- I love poultry but hate eating eggs. I just don't like them. I got a bad egg like 30 years ago and have never been able to stand them since. I eat them only rarely, so I have a lot of eggs I need to find homes for.
I started searching out specialty bakeries (nothing beats duck eggs in baking), then moved on to Asian food markets (big demand for duck eggs in Oriental cuisine), and then to health food stores. I printed out write-ups of nutritional info on duck eggs, and just kept pushing my product. I now can't keep up with my demand. I need to expand my duck flock next year to keep up with the demand I have created. (Get more ducks? Oh, twist my arm...)
The key to success in any endeavor is persistence. Find a niche that you can fill, and just keep at it.
Good luck.