The process of creating an illustration of a cartoon mascot character it can be splitted basically in four main parts. The conversation with the purchaser of the mascot regarding the mascot creation, the agreement, fees and contract, the rough drawings and the final creation of the illustration or illustrations.
The cost depends on many factors. Mainly on the complexity and the intended usages of the illustrations. That said, the same illustrator will normally charge much higher for one illustration if it will be used for advertising purposes worldwide without time limitation, than if the same illustration will be used in a single country by a low circulation magazine for one month. This example illustrates why an average hourly rate does not applies even to the same illustrator (in different projects).
We could might conclude that one illustrator could have different hourly rates for each project. This is more close to reality but again not accurate enough. A problem that occurs using hourly rate is that an illustrator should normally ask a higher fee per hour depending on how fast he (or she) works. But if one is extremely fast the hourly rate will increase a lot and this cost might look insane to the potential client as other illustrators ,who will (let’s assume) could deliver the exactly same quality illustrations, will have a much lower hourly fee. So we come down to the question “how accurate, if not honest too, an illustrator could be, so he (or she) could predict how many hours would probably need for each project”. We see clearly that the hourly rate should go together with the question of how many hours would need for the project to be completed. Otherwise, an hourly rate agreement would be a disadvantage either for the illustrator, either for the purchaser, depending on the case.
A low hourly rate might have the risk, for the purchaser, of a not so experienced illustrator that lacking experience and so, might can not be accurate for the hours needed as well as to not be able to deliver the desired level of quality, and as a result will might have to pay for more hours. At the other hand, a high hourly rate might have a risk, for the purchaser, in case he will ask for several corrections. In both cases, an hourly rate agreement could end with the illustrator’s disappointment as if the project ends really fast and successfully, the illustrator will end up with only a few dollars in the pocket, especially if the per hour cost was low.
Taking in consideration all these, I would suggest a per assignment, or per project cost. This is safe for the purchaser as well as for the illustrator too. Both knows the terms from the start, so there are less chances for surprises.
You can see a relative article about the usages, agreement and cost here.