zombie dogs are not that hard. if you have trouble with them it means your heading into town too soon. the general suggestions is survive in the woods for a few days to build up some combat skills and get some better eq. i never though zombie dogs were that big of a deal. remember rocks are your friend early on. grab them and train throwing. so you can always have something to use for range combat.
How do you get equipment or water while living in the woods? Meat, sure, but there's no clothing out there, and if you find water you've usually found dragonflies as well.
EDIT: I just went from half health, to dead, from a single dog. 2 skill in cutting and a combat knife (via the military recruit profession) and I couldn't kill a dog. And heaven knows you can't run... They're unusually impossible to actually hit, all my attacks flat out missed...
the only real priority you have early is water. everything else can wait. food is easy. you dont need cloths early. its better to train against easier stuff. now as far as water goes. you can usually find some bottled water on science corpses to get you through a couple of days. stick to eating fruit as much as possible since that gives some water. i always start with night vision. generally you can find a working toilet in a house on the edge of town. break a window in back, get in, get water and get out. at a minimum you can make it to the first night before going to town and spend the day wandering and training. throw rocks at everything you pass to get throwing to level 2. that helps alot with dogs. rocks can be picked up and dropped as you go.
in most games you should be able to find enough water on corpses to make it to the 2nd night without going to town if you also try to exclusive eat fruit as well to get a little water. you may be 'thirsty', but it wont be that bad. by the 2nd day you can have throw to 2, dodge to 1-2, melee to 1-2. if you find a corpse you find some stuff you can wear to carry a few more things. so you can carry more rocks. that is generally enough to hit a house on the outskirts at night for water. then go back to the same house for water. in .8 houses run out of water, so its a hassle, but your goal is to stay out of town until you get those combat skills up. everything else can wait. throwing is really easy to train since you can throw rocks at rabbits.
bows used to be the way to go, but they are harder to train now and are not good until high levels. so id focus on throw and melee early. during the day wander far and wide outside to try to find as many corpses as possible. sometimes you get lucky and find houses in the wild.
you can stick to just the outskirts of town at night for water basically indefinitely... until you feel comfortable going to town. i dont find dogs a big deal. i find having rocks with me to be a big bonus and training it up. by level 3 throwing they do pretty decent damage and there are so many of them, i can let zombies chase me. throw, retreat, grab more. weaken, then try to kill the ones that get ahead in 1-2 hits in melee after weakening before i get surrounded.
throwing rocks is very useful for early game survival.
btw, your lets play video is pretty good.