At 1k RMS you should be fine IMO. Stock alternator on a base car is still 175A which is pretty stout.
I would hook it all up and see what your voltage drop is like before sinking any money into the charging system that you might not have to. Wont be any more expensive to upgrade after the fact. If you do end up needing to though I highly recommend Singer alternators, they are the only company that offers an HO alternator for our cars (with several options from 200-380A). And I'd recommend an AGM battery up front. XS D4700 fits perfectly.
I have 8kW and run a Singer 380A with an XS D4700 and D3100.
All in all though, I think you'll be fine without upgrading anything. Your interior dome lights may dim a little if your at idle and blasting, but that's not a a big deal really. The rest of your lights are LED so they wont dim with minor voltage drop.