The Gaming Intelligence Agency has been online since 1998. It featured news and fan content for a long time, then moved to social media for a time. As of 2015, they don't appear to post anymore.
However, they have archives of the site all the way back to the beginning. One of those pages contains the artwork of artist "Red Leader". According to the description, Red Leader saw trailers for the newly announced Dinosaur Planet and decided to make the first fanart in the world for the game, featuring Krystal of course!
Now we get into the tricky question: is this the oldest Krystal fanart? Or even is it the first Dinosaur Planet fanart, as the artist claims? It's hard to say. There is no date on the page to indicate exactly when it was posted. There's some stiff competition to beat out the work of Leah from Nevada, our current oldest Krystal fanart champion. Red Leader would have had to create this fanart after April 29th, 2000 (Dinosaur Planet's existence revealed), but before July 26th, 2000 (Leah's postmark). It is certainly possible. Alas, without some additional information, I can't confirm it. The Wayback Machine's archive of the page only goes back to November 2000, and the gallery page archive only goes back to October 2000. I just don't know.
I will contact The Gaming Intelligence Agency about more specific date records for this work. Oh, and if anyone knows how to contact the original artist Red Leader, let me know!
Thanks to Sunnyside for the heads up!