In the following link you will find a lot of recipes. Please check them. They are in Japanese though.
Btw, you can use white wine instead of mirin, and konbu weed instead of dashi. But I would not use dashi at all. You can surely do without it. (I do not like dashi too much).
As long as you have sugar and shouyu for the tamago, and sugar and vinegar for the rice, it will come out well I think. It will taste good.