I agree with NoSquirrels.
In general I would say that the non-working (on that day) parent should take school runs. But MAN ALIVE they are boring and thankless. And you work weekends (so although I'm guessing he's in full charge, no doesn't have a school run). AND yours sound like a peculiarly cruel and unusual punishment.
I'm also assuming you don't have a spare hour for a run in the middle of the day (since you have a little one?).
What are his typical working hours? In my company the basic hours are eight hours, including a lunch break; I'd guess this is fairly typical. If he is working 8.30-4.30, then cooks tea for the children, YWBU to ask him to do the school run. If he's working 8-6pm with meetings that sometimes run late, I would not expect him to do the school run.
If, as I suspect, he's contracted to work 9.30-5.30, logs in at 8.25 but then potters about making tea and reading The Week and runs 10k at lunch, he could do a few school runs per week.
If only to take some of the strain. The fact is, having children requires you to make compromises on your "spare" time... i.e. you can't have it all! You can't lie in, read the newspaper at your leisure, go for a run and enjoy a long bath. You can pick ONE. Maybe two if your children are older. And that's the same if you work or not – assuming you enjoy an equal partnership.
The best thing I've learnt from Mumsnet is: look at your leisure time. If you have the same amount (at different times), it's probably fair.