I did the LT last summer, so I'm really excited for you. I'd love to take some time off and do it again this year, but alas that isn't going to happen. I see a lot of familiar choices in your gear list. I ended up sitting right around the 12 lb mark as well, though over the course of the trail I came up with some thoughts that could bring me lower.
Some thoughts on your gear. First of all, don't let anyone talk you out of the Sawyer filter setup. I had mine set up inline, and it was fantastic. I was always the first one drinking after a water stop! I used a pair of 2L Platy's, too, and it was a great setup for backflushing. Honestly, though, I rarely used the second for anything else. One thing you should think about is your hose arrangement. My first town stop in Manchester Center I went straight to he Mountain Goat and bought a hose splitter. It was horribly inconvenient without that. And lose the Gatorade bottle. Totally unnecessary.
Second, the hammock might be a little heavy, but it's absolutely the way to go on the LT. I used a tarptent, and I can't tell you how many times I wished I'd had a hammock. New England is a rocky place, and the LT doesn't have a lot of nice flat ground. But it has tons of trees! You won't be sorry. The sleeping bag will be a little warm for this trip, but you probably aren't going to find a lighter bag at any temp rating. I wished I'd had a quilt, for the flexibility, but you won't be unhappy. The pillow is a bit overkill. I used the Walmart floatie pillow I found in the forums here, and it was heaven for an ounce. Definitely a good alternative to the Thermarest one.
The alcohol stove is a great choice. Plenty of alcohol available in town when you stop. I also like the towel. I brought a small section of camp towel to dry rain and condensation from my tarptent, and I used it every day.
I had no problems with bugs. Like you, I brought a head net, but never took it out. Other people have told other stories, but my headnet and Deet went unused (the way I pefer). For reference, I left July 5 and went north.
As far as clothing goes, I had a pair of running shorts with no pant legs, and the only thing I ever wanted to change about it was to get lighter shorts. Your experience may be different. I used an umbrella for rain, which got me stares of intense jealousy from people I passed (2009 appears to have been one of the rainiest summers on record), and found that I barely used my Golite Wisp shirt as a result. I threw it on a few times in the morning, but that was it. The only time I wore the wind pants was when I did laundry in town.
One thing I don't see on your list is a vest. It never got cold on the LT, but it got just chilly enough that I wore my Montbell Thermawrap vest every night and every morning. I also brought a pair of thin running gloves and a beanie that got used almost daily. I didn't have a hoody, though, and simply don't tend to wear (very) dirty socks on my hands while eating.
I, too, used an Ohm on the trail. Awesome pack, you won't regret it. However, mine developed a few problems along the way. Be prepared to spend some time thinking about trail maintenance issues. For example, both my hip pockets pulled loose at the bottom and started flopping around, the eyelets on the side sock cords pulled out, and the frame tube stitching broke. Nothing major, and nothing I couldn't handle, but worth thinking about in advance.
I wholeheartedly agree with Chris about the leatherman and the iPhone. I used a Spyderco Ladybug, and I could have gone with a smaller and lighter knife if I could find one. I highly doubt you'll need any more than that. The iPhone? An absolute waste. Take it from a guy who carried his iPhone for the whole trail last year... that's a significant weight savings that you just don't need. Plus, the northern half of the LT is a lot of slick steep rock. You're going to take a few tumbles. You don't want to be worried about that glass screen every time you do. Also, as you must know already, the battery doesn't last at all. The charger is cute, but it doesn't do you much good in the woods. If you must have a phone, buy a cheap light Nokia off Craigslist. Oh, and the iPhone takes unacceptable pictures on top of it! If you want to take photos, you're going to need a camera. Sorry to be the bearer of bad news, but don't make the same mistake I did.
As for the dog, I wouldn't worry too much. Plenty of people bring their dogs. You may have to carry him up a ladder or two, but you'll be happy to have the companionship. Generally, he'll be at home on the LT. My buddy joined me for a weekend with his lab, and I couldn't believe some of the rocks he ran up and down. Your pup is going to love it.
Feel free to reach out if you want any beta about the trail or my gear. More than happy to share my thoughts.