What year is it mate? Judging from the RSU forks and plastics is circa 1996 or 1997?
Looking at pics, you might be missing a voltage regulator which is needed to power up the lights, the horn is respective of AC or DC, those bastards just needs power from the stator.
I have a wiring diagram which is pretty common for majority of that era husqvarna, some differences but fairly similar:
https://drive.google.com/file/d/0B1gFSeW1F5xIZXpnYjlGSWtWQk0/view?usp=sharing
If in doubt (dunno where ya from in Melb), but take to a bike shop or auto elect and they can have the whole system working for you so that all you need to do is to plug things off and on when you go for a ride in the bush...reading wiring diagrams can induce heart failure
As for rec reg, need 1 RHS mirror, front and back lights, brake light and number plate light (you can fit those aftermarket LED units), no need for indicators unless you want full road reg. As far as Vicroads inspection, they are slack and you could leave the bike on the trailer and they'll just look over the VIN and engine number. However, our mates VicPol can make life hard for you when they stop you in the bush about your lights not working but majority of the time they are fairly cool with it so long as the you and the bike are regoed.
Full road reg, same as your CBR600, chain guard, two mirrors, indicators as well as the a proper RWC from a shop...not hard to do just cost you $500 in rego compared to $78 in rec reg yearly?
For what its worth, you can do the dodgy that MX bikes do, is to fit a small battery and switch which allows to system to work, l say it's dodgy because for either registration, the whole system cannot be a total loss system meaning the lights are reliant on a battery source rather than powered by the operation of the vehicle. Anyway, lights are great in the bush to avoid head on's and the horn great to tell ya mates where you are
I think the carb on that bike is a Mikuni, do search in the 2T area as there are plenty of guys with Mikuni setup's on this forum and the common theme is to first check the float height.
Congrats on the bike BTW
