Should! I'm currently rocking a '07 M5odR1HD trans in my '01. There aren't any differences in manuals...just be sure to stick with '01+ 3.0 2wd for your '03 3.0 2wd.
Check out car-part.com. It's an online database of auto recyclers and their inventories...it can be narrowed down to region too. That's how I located my new engine and the trans when I needed it. There may be multiple options in trans even after opting the 3.0, year range, and drive. These are based off the factory build sticker and what that actually tells you, I haven't a clue. Paid little attention to it when I needed a new one.
PS: I've got the HD that came behind the '01+ 4.0's.......they're weak. I'm on my third. lol.
'01 XLT disguised as a '03 Fx4 Level II
Big. Loud. Slow. Bright.