Bob Kerry, in his guidebook "Backcountry Rockclimbing in Southern Arizona", gives Moby Dick a three star rating and it is considered to be a Cochise Stronghold classic. The climb is a moderate climb on the Whale Dome with the crux being rated 5.8. The lower pitches protect well but the upper pitches, although fairly easy, are runout. To get off the dome, there is an invigorating rappel. Bob Kerry describes it as "...a classic, hairy rappel; a scary (but safe) start and all air."
Keith Haskell has an excellent trip report with many photos of the route. He has a detailed description of the climb, describes the emotions of his group, and has a large number of photographs on all aspects of Moby Dick. Between his photos and mine, virtually the entire route is covered.
Directions and topos to Moby Dick can be found in "Backcountry Rockclimbing in Southern Arizona" by Bob Kerry or "A Falcon Guide: Rock Climbing Arizona" by Stewart M. Green.
Warning: Gear belays and gear placement are shown in the photos below. The gear belays and gear placement shown in these photos should not be considered safe. Use your own judgement if you do the climb. The second belay is especially tenuous. There are not many options for gear placement at this belay. The strongest feature at this belay is a small tree that would probably pull if a packrat took a fall on it.
Warning: If 5.8 is at your limit for leading, Moby Dick is probably not for you. There are long runouts high on the climb and you would not want to 'rap the route' if you get wigged-out. Read Keith Haskell's trip report for his description of "...mild grippage" on the upper pitches.