What do penguins have to do with Iceland? Penguins live about as far from Iceland as it gets.
But in case that's part of that joke that I'm just missing: penguins don't very very well-defined necks, so it'll help if you have the bird's head just slope into the shoulders instead of having a narrower neck area.
Also, they have shorter flippers. The flippers here are very long and blend with the body. If you make them shorter and don't have them go in towards the body, they'll read more clearly as flippers. As-is, it reads like a fat armless body instead, because the flippers read as part of the torso.

I feel like that video is better example of "lackluster work is always easy to do" than of what newer technology can let us do with the same amount of effort. I look at that video and see the same problem in it that I see in many indie pixel art games: uninteresting art direction. Pixels for the sake of pixels is just as boring and pointless as advanced rendering techniques that are there just to be there, rather than to add to the experience. That said, high-res art (3D and 2D) combined with solid art direction and skill is more versatile than pixel art, simply because it's less limited.

So, why do pixel art at all? Because it's fun. Because it's a puzzle*. Because it can teach you about colour and composition faster than working in HD can. Because it's what I feel fits the thing I want to make. Because of whatever other reasons an artist might have, even if I might think they're weird :] Why should it need to be innovative or useful? Portrait and landscape painting lost much of its practical usefulness and financial viability with the spread of photography and never recovered. Photography precipitated more abstract art as an attempt to keep painting relevant and innovative, which I think is equivalent to those "non-traditional" pixel art games RAV mentioned. But has portrait/landscape painting become obsolete or worthless? No, because it's still enjoyable and because there are still projects for which it's a good fit for various reasons. It's the same with pixel art. These kinds of threads try to find some deeper meaning and use to it every single time, and I just don't see the point.

What makes pixel art a good fit for a project when technology isn't the limiting factor is an interesting question, and I'm glad this thread has already touched on it. I feel like this is another one of those things that will differ from artist to artist, since each artist's reasons for liking pixel art are different. For some people, the strengths come from the reuse. For some, the strengths are the relative ease of creative cohesive visuals due to the limited palettes. For some, it's the nostalgia factor.
My own pixel art games are pixel art because I have the most fun making pixel art as opposed to the other options available to me, and because pixel art sufficiently conveys what I want to convey in those games. When met with a project for which pixel art isn't the best option (factoring "will I enjoy making it" into account), I don't use pixel art, simple as that.


* I wanted to touch on the "puzzle" aspect of pixel art that nessx007 mentioned. I agree with that assessment, but I don't feel it's unique to pixel art. My main medium is comics, and comics are absolutely puzzles to solve! I think most (if not all) kinds of art are comparable to puzzles, it's just more obvious with comics and pixel art because there are fewer pieces to work with, and therefore fewer successful combinations. Among my comic artist buddies, "I need to solve this comic page" and "I can't figure out [how to solve] this panel" are a fairly common turns of phrase.

You should post your previous attempts and explain what you didn't like about them.
It would also help if you posted some context. Are there any environment tiles done? Any enemy sprites? If not, it may help you to do some of that, as they will give you a sense of direction for the player sprite. The player sprite should stand out from their surroundings, so having some environment work done (even if it's just rough, unpolished mockups) will help you with the colours and detail level. It'll also help you with the perspective on the characters.

16x24 is pretty small, so for the sake readability, it may not be the best idea to do very realistic proportions, as you'll end up with a very skinny sprite that leaves very little room for colour/value identity and defining features. Be prepared to stylise things to make the sprite easy to see and identify, especially in combat.

I also don't like the characters cluttering up the logo. Place them below the logo in a row, perhaps? If you want to the characters doing something interesting, then have them interact with each other, but try to avoid having them actually overlap the logo more than a teeny bit, because otherwise it just looks too busy.