You CAN easily do it yourself, but I wouldn't. Get on record going to the dealer for the first checkup, then do the 6000 yourself. Helps to have a dealer record should warranty claims arise, and they will usually come up in the first few thousand miles, if ever.
There is no harm doing the service between 500 and 800 miles. In fact, my dealer prefers the longer interval. I had mine done at 650 miles.
Monte