Well, if it's still kind of a secret project you can keep it that way for now without any issues. Since it's story-driven I would wait with an announcement until all* of said story is represented within the game (since while the current gameplay looks serviceable, right now there's no indication that this will have more than a few textboxes worth of story - if any). Because if that announcement really takes off but you need to move apartments/houses, be hospitalized, get writer's block or fall into depression, then much of that momentum you might have gained would be lost. If you have a look at the MMORPG-scene there's never a shortage of announcements, Kickstarters, and the like but often enough a project takes longer than expected or gets cancelled which leaves a lot of bitter people (like me!♥) who will grow very weary of "announcements" that don't at least have actual gameplay that they can show off. ("Look at this single character walking in a straight line through an alley of trees without any other characters/mobs in sight. Aren't you impressed by our shaders?" is kind of a trope when it comes to MMORPG-announcement trailers.)
Sorry if that was too much of a tangent...

I think having some kind of teaser for your game less than a month before it comes out could help raise interest. But my personal advice would be to delay said teaser until you already have something that is at least flawed but entertaining nonetheless - that way you will still have something to show for if life gets in the way.

Also a bit of unsolicited advice: Get a friend to check out your game every now and then. They don't have to approach it like professional tester - just let them dick around in it without giving them directions and ask them what they thought. And if they tell you something along the lines of "Yeah, it's good...", then you have either kind friends who are either terrible liars or exceptionally bad at expressing their thoughts and opinions. :)

* (or if it's on the scale of Money Island 2: most of the story)