Is this a lot for a Christmas and Birthday present combined?

I've always wanted a gaming PC ever since I got Minecraft in 2010. (Nerd, I know.) I'm 14 and love games to death, but the problem is that I come from a barely middle-class family. Don't get me wrong though, I love my family, but I've had to skip out on a few Christmas's. I've always played with low FPS and stuff in games and it's been pretty stressing, so I've been wondering if the Alienware Alpha (i3) was too much to ask for. It's ranging in the $400 range and the laptop I play on now is my brothers, which was like $300, and I also got it in like 2011. My birthday is on Janurary 29th, which is sort of right after Christmas, so I was thinking if I just got the computer (and things like the monitor, keyboard, and mouse), I didn't need to get another thing for my birthday. Thoughts?

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