Can i access my minecraft account on another computer?

I have a minecraft account, and downloaded the game in my current computer. I have been playing my minecraft under the same computer ever since i got the game. However in a few days i'm getting a new computer, and i would really like to be able to access my current minecraft account on that computer when i get it. I know i have to re-download the game on the new computer when i get it, but does that mean i have to make a new account as well? I'm new to this, i do not know much, i'm sorry of this question may sound "dumb" in any way. Also i have a few minecraft worlds. When i get a new computer, and if i'm able to access my old account, will i be able to play in the worlds that i already made? Or do i have to start over?

You don't need to create a new account or start over; you can log in with the same account details and be back in the game in no time. However, you will lose any worlds unless you transfer them from your old computer to the new one.

Worlds are saved under %appdata%\.minecraft along with all your other Minecraft data. Copy and paste into the search bar to access the directory on your harddrive.