To force carb your 1.5 gallons you will want to siphon it in to the keg, not pour it. Hit the keg with about 30PSI, and purge a few times to get all of the O2 out of the keg. This will keep you from oxygenating your "Champagne". After that give it a good rolling around on the floor at that 30psi for about 3-4 minutes. Hit it with the CO2 again at 30PSI and repeat the floor rolling procedure. Purge the keg and set it to your serving pressure, usually 6-10PSI and let it settle down in the kegerator for an hour or so. This works for me, YMMV.
As for the kit it looks like it has pretty much everything you need. You can do 5 gallon full boils and overall make a better end product than you did with the Mr. Beer kit. My only recommendations are that your primary fermenter shouldn't have a spigot and you should pick up an autosiphon for transfers from your fermenter to the kegs. I would also pick up some OxyClean Free for cleaning, and some StarSan for sanitizing, you won't be sorry!
Welcome to the obsession!!!