You need to figure out (at least roughly) what it will cost you to make this cake. I know it varies in different areas but generally cream cheese frosting and carrot cake are a little more costly to make than your basic chocolate and buttercream. Next you need to factor in the time you'll be putting into making this cake, and figure out some sort of hourly wage and factor that in as well.
Or you could look at bakeries in your area and see what they charge per serving for custom cakes. Then you can decide whether you want to charge more, less, or the same.
Or, the way I do it with family and friends is I just charge cost plus tip. I'll say "Hey my cost on this was $, so whatever you think is fair." I've never been disappointed!