I also think you are singing below your natural optimal pitch. I'm a sucker for singing and playing at the same time, there is a thing that happens when you start to weave the guitar with your voice and your in charge of both of them that never happens -- can't -- with individual tracks. Even very beginning singer/players have a charm when they do this for me. And I find it very personal and even moving.
My comments are going to be about the singing. I think you should stick with this song for a while and get it to the point where you know the lyrics so well you could sing it in your sleep. Then think about the song and what it means, or doesn't mean, to you. Then have another go when you are in a key better for you, probably at least two steps up? You can move it a half step at a time with a capo at first til you find the right place. Don't be in a hurry.
Playing and singing together are a performance art, and to perform you need to have intention. Intention to do what? Communicate something. What are you wanting to say? This is more important than pitchiness or timing or anything else.
Maybe someone will jump on board now and say that this is only one way to go. That you don't have to know a song well, or sing anything but the notes and words to have it work. That intention and preparation are overthinking it. That alot of songs are not the sort you can give meaning to. Maybe, maybe not. This song can have meaning anyway. And for me, while I'm not great at it yet, I believe it is the more rewarding way to go if you want to have a deep and meaningful experience singing a song. And when there is that connection between meaning and music and words, you will feel something special happen. You will.