I think you need quite a few other items.
Protection from rain. In the past when I've camped there it was mostly dry. IIRC, it did rain a little the last time I was the Grand Canyon. But not having some sort of rain gear isn't a good idea. You can get a plastic poncho for a buck or two. They're small and weigh next to nothing.
Bath towel to dry off if necessary. (Put in garbage bag. It'll keep it dry, or if you've used it and it's a bit wet the garbage bag will keep your others items in the pack dry.)
Plastic garbage bags. I line the inside of my backpack with one to ensure things stay dry. And of course you'll need them for garbage.
Knife, rope/cord and duct tape. Knife should be self explanatory. The others for emergency repairs etc.
Portable propane stove. Don't rely on being able to have a campfire unless you've really checked out the rules. Even if generally allowed they are sometimes temporarily forbidden because of drought or high winds. You may not be able to find sufficient dead wood laying around, not close anyway. Hot food never tastes better than when you're camping. Don't forget utensils. Can opener? Corkscrew? etc.
Water? Where will you get sufficient potable water and where will you store it at the campsite? A canteen is for a hike, not a camping trip. They make collapsible water containers for camping. When it's empty it won't take up much space etc.
Paper towels. toilet paper. Soap.
Chair? What are you going to sit on? IMO, standing or sitting on the ground or a big rock all the time sucks. Inexpensive lightweight portable camping seats/chairs are available.
Flashlight? OK. A lantern is better. Also useful are those little flashlights on a headband. Let's you use both hands when doing a task at night in the dark or even just walking around. They're cheap. Might carry a few extra batteries too. Murphy's Law never fails to disappoint.
Compass? Do you know how to use one?
Put your lighter, if that's what you're using to start fires, in a zip lock baggy so it won't get wet.
Maps? Ziplock baggy too.
First aid kit. I include one of those 'space blankets'. Looks a little like alum foil, weighs nothing, is smaller than a cigarette pack and costs $1. It's suppose to keep 100% of your body in and is waterproof. Carry them if you go hiking away from the campsite in case you get lost.
If you're going to take day hikes away from camp I suggest you make up a list of items to carry in case you get lost. The space blanket, lighter etc, a whistle, map, water, knife, flashlight, power bars etc are things to consider. Nobody ever plans on getting lost, but shiz happens.
Enjoy your trip.
Edit: It's always better to get these things ahead of time at a Walmart etc. Buying stuff at touristy places get expensive.
Fern