First of all, I'd like to say that the art style is looking fantastic. It really brings me back in the day, I really love the 8-bit colors you used, it looks extremely promising so far.
Now for the critique part... The game is called Dwarf Miner, this insinuates that the game is about mining. This on it's own isn't really a bad thing, except for the fact that this has been done so many times it becomes rather cliché. I enjoyed mining games, like Minecraft, Terraria or the smaller Flash games with a similar idea, but it starts to get just really unoriginal. That said, I do think you should be fine if you implement some of your own original features.
The game-play seems very slow paced at the moment. Even though I understand that this might be a game that's made for more casual purposes, a bit faster gaming would be nicer. Only fastening your movement slightly could make it a much better game. In my opinion that is.
Although I praised your artistic side before, it does have a big flaw; the styles don't blend well. Right now, the heart really looks off, as do the mountains. What I would have done is perhaps erase some colors and try to keep to shading a bit more basic.
Overall, it's looking quite good so far, although the demo is really short so far, it's looking great. Please don't take my criticism too harsh and keep in mind that all I've said is just my opinion and I don't speak for others.
Keep doing what you're doing.