Before I give you a list, I'd just like to point out that, having never cantered or galloped before, you'd still be considered a beginner rider, not an intermediate. :]
Anyway, list. This summer will be my 5 year going away to camp (1 week the first year, 2 weeks 2nd and 3rd years, 1 month last year and this year as a Riding Instructor in Training). Most camps /will/ send out lists of what you can/should/can't bring, but that's usually more towards the summer.
Jeans-I would definately bring more than 3 pairs. If you're going to be there for a week and riding every day, then they're going to start to get pretty gross pretty fast...and definately more bras. Again, riding every day, it's going to be hot, you're going to get sweaty...yeah. Bring more.
T-shirts and tank tops
Riding Boots, flip flops, tennis shoes
Helmet (if you have one-if not, the camp should have some for you to borrow)
Sweatshirts
Bathing suit
Shorts/capris
Sweatpants
Bandanas/baseball caps
Sunglasses
Rain poncho
Watch (I always bring one since I'm a RIT and we have to keep on schedule all day)
Sleeping bag, sheets, pillows
Hairbrush, hair ties, hair clips, headbands
Toothbrush, toothpaste, floss
Deodorant
Chapstick
Razor/extra blades (for a week you should be fine with 1)
Nail file, nail scissors, nail clippers-I keep my nails kinda long, and since I'm working the whole time I'm there, they tend to get pretty chipped and banged up, and I hate scragglies :P
Shampoo, conditioner, body wash (I bring the whole bottle to go for a month)
2 Body towels, 2 hand towels, 2 wash cloths, plus a beach towel (for a week, you'd be find with 1 of each)
Bugspray
Sunscreen!
Anti-itch lotion
Backpack
Books, magazines, spiral notebooks, pens and pencils
Cards
Flashlight/batteries
Gum
Waterbottle
I'd check with the camp about the snacks, candy, and Ibuprofen; the camp I go to doesn't allow food in the bunks because of bugs (RITs are allowed to bring a box of food for our out-nights, but we keep them in the kitchen), and most will also have a camp nurse that keeps all of the meds so they can keep track of who's taking what when, and why they're taking it.