Even though your question was more geared to online poker, I'm going to give my own experience in both online and brick-and-mortar play. I'm also limiting myself to limit because, even though NL is probably more profitable, it's riskier to get started in. Apologies if I'm answering questions you didn't ask.
As a newbie myself (~1 year), I'd say that you should be able to beat low-limit casino games and micro-limit online games after only a few months of "serious hobby" study (5-10 hrs/week, say). You will probably also be able to beat the higher online limits (1/2, 2/4, 3/6) but i don't have experience there so i depend on others' input to form that impression.
The very very hard part is, poker is so high variance that you should EXPECT to go through a big downswing where you WILL question whether you're playing correctly, even though you most likely are playing much better than your opponents. If you've gone through a couple of those in microlimits beforehand, then you'll be less likely to panic when it happens in the more expensive games. I don't know how the variance in Blackjack is, so I can't compare them.
A couple of great resources I got off this forum were:
[img]/images/graemlins/diamond.gif[/img] Mangatang's page at
http://www.kingscascade.com/Poker.html , especially the regimen linked under "Playing Online". I don't think you'll want to wait so long to build up a bankroll, since you already have at least $2K available with more to come once you're confident in your ability. But you probably should play microlimits until you're +100 big bets or so, just to convince yourself that you're playing well (and all those clowns drawing out on you are really playing badly!).
[img]/images/graemlins/diamond.gif[/img] A great spreadsheet that simulates poker's "random walk" I forget where I found it on here, but my copy is named Streaks.xls so perhaps you could search on that.
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So, over the past month, I've bought 10-12 poker books -- pretty much all the standards (I tend to really dive into things).
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Heheh... sounds familiar.
HTH. I look forward to more experienced players' answers. Good luck!