Would this be everyday? Would it be some days to activities and other days bring your child to your job? If the person takes your child to activities, would they stay with your child and then bring them home (or to your job) afterwards or would you be picking your child up after his or her activities?
I think a weekly rate would be better than hourly. When I did a similar arrangement— I would pick 2 kids up from the bus stop and take them to their activities (stay there) and then bring them home- this was a Mon-Friday gig, and some times, I had to drop one off and take the other child to their activities and then go back and pick the other child up and then take them home. My weekly rate was $250 for about 2-3 hrs per day (it varied). For something like your arrangement but depending on how far/long the commute- I would do maybe $150-180 a week?