Short answer: Yes your document should be 1920 x 1080 (I can't think of a longer answer for this cause I don't know what else is needed)
What I wanted to dig into is that 5000:1 cause I have a hunch you don't know what that means either. That's called the contrast ratio.
It's a new development for LCDs - “dynamic contrast ratio,” which has a value significantly greater than the “static” contrast ratios encountered in traditional LCD monitors.
DCR can achieve a value in the 5000:1 to 10000:1 range and is desirable for home use, where displays are used for gaming and movies...sooo, what this is actually saying is that the white areas (the brightness when the video inputs are at their maximum value) are 5000 times the brightness of the "black" (all video inputs at their minimum).