Power Problem

I just recently purchased a 130 amp alternator and a brand new 1k amp battery for my '92 mustang. Im running about 1k watts for my soundsytem. I am still not running up to par on volts and only hitting about 11.8 at idle without the radio on. I don't know if its the alternator or the battery or just the whole system. Should I upgrade to a high output alternator with 1/4 inch studs for better conductivity and external regulators with another battery in the trunk. What would I do with the factory plug for the alternator, theres two plugs and I noticed on all the aftermarket ones there are no plugs. You say to upgrade the wire size to the battery, is that wire in one of the factory plugs that went into the factory alternator? Just wondering what my options are, any help would be greatly appreciated, Thanks

Running two amplifiers for my soundsystem but even with the amps disconnected I am still having a under voltage problem.
The volt reading is from a digital reading on my cd player and is consistent with the one in the dash..
No I haven't changed the wire from the alt to the batt, if i change the wire I would have to get a new plug for the alternator ?

ran new power wire, works perfect, thanks