I've survived several werebeast infections in this build and it all comes down to being prepared.
Werebeasts enter the map in stealth. The notification is deceptive, by the time you get it the werebeast has already had enough time to bite and infect several dwarves in a covert manner. Protecting your entrance and ground floor with wooden palisades and putting dogs on the entrance will reveal the werebeast before it has a chance of starting an outbreak.
Your staring hunter already has enough skills to kill the initial werebeast from a safe distance.
If you suspect one of your above-ground dwarves is infected, immediately activate your burrow and raise the bridge, stranding the potential carrier outside until the full moon.
If you notice any dwarves trying to covertly kill your own dogs, wall them in inside their rooms. Same goes for any dwarves with suspicious injuries.
After more than 2 dwarves have been infected, the disease will spread in an exponential manner. Your military dwarves and hunters can always survive by keping out, laying low, and making a list and checking it twice. Your civilian population is pretty much doomed, but as long as you can kill or wall off all of the infected and keep one hunter alive you can keep the fort going.
Pretty sure a good chunk of this is wrong. Werebeasts don't enter the map in stealth, you just don't know they're werebeasts until the lunar cycle. I would say that it is very rare to get a notification only after someone has been bit, though when you *do* get the notification, be prepared to lose the closest dwarf or two depending on where your military is.
Archers are of course the preferred method of were-beast murder, but your woodcutter, drafted, will likely turn the werecreature into werecreature new york strip. Miners are pretty good too, but they need a relatively lucky shot to avoid biting. Chopping weapons have a tendency to remove limbs, reducing the speed of the creature, and therefore exposing yourself to fewer potential infections.
As far as initial military, I usually try to smelt an axe or two out of any metal I can find ASAP. This is usually pretty easy, digging out a sizeable stockpile and your bedrooms/initial workrooms is very likely to net you some tetrahedrite, and if you throw up a smelter and a wood burner along with your first mason's shop, you can get four axes out of a single ore. Then make about a dozen wooden shields. Then pick the two most useless dwarves from the *first* migrant wave and give them an axe and a shield. Wooden shields are nice because they're very light and super cheap, though they will usually not last very long. I try to maintain a surplus of available shields at all times, because even a minor skirmish results in the destruction of most of the worn shields. Shields will occasionally block bites.
The most important bit is to limit the spread of infection. This is somewhat time-consuming. Once the mayhem is over and the werebeast is dead, you need to read every combat report. Every single one, from every person involved, not just the werebeast combat reports. If you see "The werecreature bites Urist McStabby in the 4th left toe (or whatever)" then it is safe to assume that the dwarf is infected. For early military without armor and skills, this usually means every dwarf sent will get bit. It may be advisable to only send one or two dwarves to limit potential bites. Anyway, for the dwarves that have been bitten, you have exactly one month to deal with them. This can be done in a few ways. I usually add them all to a squad, order them to all stand in a room a bit out of the way, and wall them in with a single pick. As transformations don't all occur simultaneously, eventually all but one dwarf will be dead. That dwarf will never die. If you left him a pick, now's a great time to do some single dwarf fortress inside your fortress. I usually make him start by building tombs for all of his comrades, which also need to be walled off from the infected dwarf. That dwarf has until the end of the earth to do it, though. Or you could individually wall the bit dwarves into their own rooms, if you don't want them killing each other. If you have a werebeast legendary armorsmith, for example. Making him useful while keeping him isolated might get !!FUN!! however. Just don't use doors or anything, werebeasts are building destroyers. Plus, now that you have a werebeast permanently in your walls, your fortress will never crumble. Everyone else could die, but your weredwarf will live on.
Don't know anything about the dogs thing, that's new to me. As far as I know, infected dwarves are perfectly normal as long as there is no full moon. That's why I usually give my infected a pick, so they can put up a masons furnace and build some mugs or something to keep themselves happy. Insanity is still a possible issue. If they go berserk, you can take the walls down when they're in dwarf form and have your military kill them safe from risk of infection.
Finally, I've found that if you have those two axedwarves training from the first migrant wave, then a rapid expansion of wealth and population to about ~80 is in order. Personally, I prefer sieges and cyclops to ambushes/werecreatures because they announce themselves and give me time to get the civilians out of the way. At a population of 80, I find that you get a lot fewer minor attacks in favor of somewhat consistent sieges. Just make your initial two axedwarves squad leaders for the entire 4th and 5th migration wave.