You have a good start, but there are some issues.
First, I want to applaud you for actually using some edge looping which I sadly don't see enough of from many anim8or users. So good job there. But, you have way too many faces! In fact, it looks like you split every face into 4 faces! There's no need for that. And once you narrow it down, you could still get rid of a few edge loops to minimize the face count even more. You can then make it a subdivision object which will smooth it how you want, yet you can keep the base mesh more simplified giving you much more control and better results.
Good start, I look forward to what you do with this.