It doesn't matter when you get there (well, unless you're so late that the market is flooded and it's impossible to get your name out there). If you were to be first to launch, they'd come after you with overlapping features. Then what? And what about another company that comes to try to take advantage of the same space? And another after that...

If it truly is a good market, it will be crowded soon. As long as you aren't entering a crowded market (and one competitor is not crowded) than I'd go for it. This assumes you can do a better job than the competitor and have something to differentiate yourself with. If you are truly overlapping than pivot. Hell, even a change in your marketing strategy alone could be tremendous. Just differentiate through the way you position and brand your product.

You do have only a months work into this, so feel free to abandon it. However, if you get into the habit of abandoning anything where you're not first to the market... I can only assume you'll never go towards anything because, let's face it, what are the odds you'll ever be first in something entirely new? Very slim.