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It is possible to create a new delivery service (A&N has one) but not simple. First you'll need a new phone call to order the item, then a new service sim type to answer the call and make the delivery. Service sims that arrive in a vehicle are generally controlled by the vehicle so you will need to create/clone a new delivery vehicle.
The default delivery truck however is capable of being used to do lot more than what it currently does do, it has built in support to deliver almost anything. If you don't mind the food being delivered in that blue truck by the default delivery driver then that would be the best place to begin. A new phone call and perhaps a couple of minor changes to the truck is all you'd need.