There was a study which examines the exact question you posed. This study, which was conducted by Stone et al. (1999) compared accuracy of diagnosis of autism and a pervasive developmental disorder not otherwise specified (PDD-NOS).
With regard to autism, the study suggested 2 conclusions:
(1) the identification of an autism spectrum disorder can be made reliably in children below the age of 3; and (2) the specific diagnosis of autism can be made reliably in children under 3 years, as long as the diagnosticians have experience evaluating young children. The latter conclusion is presented more tentatively, given the limited sample of clinicians employed in the present study. Further study of the impact of experience on diagnostic reliability at young ages, using lager samples of clinicians, would shed additional light on the issue.
Regardless of the initial diagnosis, the large majority of children remained on the autism spectrum at the 1 year follow-up.
Of the children who received a diagnosis of autism at age 2, 96% remained on the autism spectrum at age 3, and 72% retained the specific diagnosis of autism. Although the results suggest that symptomatology improved for 28% of these children, only 1 child (4%) improved to the extent he "left" the autism spectrum.
They also pointed out that diagnostic stability did not vary as a function of whether the same or a different clinician made the Time 2 diagnosis, proving further support for the robustness of the diagnosis.
##References
Stone, W. L., Lee, E. B., Ashford, L., Brissie, J., Hepburn, S. L., Coonrod, E. E., & Weiss, B. H. (1999). Can autism be diagnosed accurately in children under 3 years?. The Journal of Child Psychology and Psychiatry and Allied Disciplines, 40(2), 219-226. doi: 10.1111/1469-7610.00435