> Frederick sent out for a hot meat-pie from the chop-house around the corner.
This could well mean that he went around the corner to place an order to be delivered. Or, as you suggest, it could mean that he offered a kid on the street some money to walk the order to the chop shop.
But even poor households in the nineteenth century would typically have had a "maid of all work," someone who worked part time to do chores, including running errands.
There are multiple possibilities, then.