When my son was in daycare, around 8 months, I'd send four 6-8 oz bottles a day. I'd nurse him in the morning before we left (around 6 am), he'd get breakfast at daycare (whatever they were eating--my son was a very good eater and ate a wide variety of foods very quickly), a bottle before morning nap, bottle when he woke up, lunch (again, what they were eating), bottle before afternoon nap, bottle when he woke up, and then snack and we'd feed him dinner at home. My boys (I now have a 9 month old at home in addition to my first, who's now 4) both have really been into eating real foods. My first preferred the bottle of pumped breastmilk to nursing, so he mostly nursed overnight and got the bulk of his milk at daycare--he was there about 7 hours and had 24-30 oz there. But--at around 8 months, both my boys were eating regular meals with the family, minus the food concerns--nuts, honey, dairy, seafood. We force the cereal on them for iron, but they both prefer meat to the cereal. We sneak it in other foods, but basically do baby cereal once a day. I KNOW we give our children more foods more readily than a lot of people. We didn't start our boys on food until 6 months, but once they got exposed, they really took off and our doctors have been fine with that. I also second what one mom said--your child might eat more at daycare. Mine did, partially because daycare made (healthy) child friendly foods--lots of fruits and spaghetti and things kids like, whereas we ate what we liked at home and tried to convince our kid to eat it. I'm rambling now, so I'm done. Good luck!
Oh--and if he's only napping a half hour there, that seems like not enough. Of course, all children are different (for both eating and sleeping) so going with what you believe for your child is probably going to be best!