I have an '03 Civic with 1.7L VTEC that I bought new. I have 9K miles on it now. My first oil change was 3900 miles (M1 5w30) and the second was at 7500 miles, also with M1. The oil has stayed pretty clean for me since new, an in-town driver. I live in TN, so we get a range of temps here.
I do track changes in oil color and I think that color change is significant to note, though not necessarily bad, and I recognize that it is unscientific.
I really don't know how to advise you since the amount of color change of oil is a very subjective thing, and may depend on the oil itself. However, I think that Hondas make pretty tight engines so I am surprised that you are observing this after 1K miles. For whatever reason, the oil on the dipstick always seems much darker when it is cold than when warm, and I think that this is due to more than simply cold oil being thicker on the dipstick.
Check for air leaks, missing air hoses, air filter seal.
Look in the oil filler and see if you see any varnish or crud building up on the valve train. If so, maybe you are running too fuel-rich.
Finally, have you added any fuel cleaners recently? Historically, I notice the oil changes color a little when I use fuel cleaner. Given this, I try to use fuel cleaner right before an oil change.
Hope this helps. Enjoy your Civic!