Axis I is correct, but I honestly think autism, and other developmental disorders, should be on Axis II. That's because Axis II is for long-term or life-long disorders--the personality disorders and mental retardation (also called intellectual disability or developmental delay, depending on where you are). Those things are in the background of other diagnoses and have long-running, relatively stable courses. I would put autism in that category as well, and also some other disorders like fetal alcohol syndrome, some congenital brain conditions, long-term TBI or stroke damage, and specific learning disabilities--the disorders that are not expected to change much over the lifetime, for which the primary treatment is therapy designed to help you deal with those problems. For these disorders, if you "lose the diagnosis", the result is that you have the symptoms but not the impairment necessary for a diagnosis, probably because you have learned enough to cope without help or accommodations.
But since I don't get to write the DSM, it's Axis I.