Tumblr, a service that lets users publish short, simple blog posts, has raised $4.5 million in a second round of funding.

That’s not a huge amount of money, but as All Things Digital’s Peter Kafka notes, it’s still impressive since the New York company is “exactly the kind of startup that’s supposed to be gasping for air in today’s dismal economy.” Namely, it’s a web company without a broad audience or a clear business model. Tumblr says it will start bringing in revenue during the first quarter of 2009 with some kind of premium service.

And while it’s still something of a niche product compared to standard blog platforms like WordPress and Blogger, and even microblogging site Twitter, that’s starting to change. Tumblr says its traffic is now six times what it was at the beginning of 2008, with 500,000 publishers drawing a total of 15 million unique monthly visitors. It’s well ahead of competitors Posterous, which launched this summer, and Pownce, which was acquired and shut down by blogging company Six Apart earlier this month, according to data from Compete. (I wouldn’t be surprised to see a sizable number of Pownce users moving over to Tumblr, too.)

This round was led by Union Square Ventures and Spark Capital, who also led Tumblr’s $750,000 first round last year.