First off, I'd recommend having 20 buy-ins for any given stakes. So get your bankroll up to $2,000 and then move up.
Bankrolls and multi-tabling is an interesting topic. Let me make one thing clear first of all:
If you're a computer, your bankroll requirements do not change because you play more tables. Playing four tables is no different than playing four times as many hands on a single table - to a computer. But you're not a computer.
You, unlike a computer, are liable to make mistakes you normally wouldn't because you play several tables. You might fold in a slightly profitable situation, or you might call where you probably wouldn't have if you had noticed earlier that this guy is a total rock. But since your EV goes down a little - per hand - when you're multi-tabling, your risk of ruin also goes up.
But, and this is the key question you should ask yourself, what's your plan for your bankroll? You can play with your entire roll at a $1k table if you have no qualms about reloading and don't care what happens to it. Not likely, though. At least I hope not. You can also play at $100 NL and sit down with effectively 40% of your stack when you start out. Note that if you get stacked at any table and re-buy, you're now sitting with half your bankroll.
Are you at that point willing to take your chips and move down to $50NL if you get stacked again? Because that's the danger of NL and multi-tabling: You can get stacked a few times in a row, and even though you may be up on some tables, you might not have enough left to buy-in at the first one. This has happened to me, and is no fun at all, heh.
I write too much. And I haven't had breakfast yet. Hungry.