One thing to keep in mind is that doing research with specific populations is quite different than working with them. If you like providing direct care and therapy to people with autism and other special needs, a developmental psychology PhD won’t really prepare you to do that. A developmental psych PhD would be good if you want to conduct research with people with special needs, particularly to contribute to the development of interventions or best practices for these folks.
But fair warning: the more advanced you get in your research career, the less time (generally speaking) you will actually spend directly working with people with special needs. As a graduate student, you may spend quite a lot of time interacting with participants; as a postdoc and new assistant professor, less; and as you become an advanced assistant and associate professor, you’ll probably be mostly supervising your own students in their interactions while you spend more time writing grants and papers. That may be okay with you if your main goal is uncovering the secrets of how developmental disabilities work and developing solutions. But if you want to do direct care, you might be interested in another career.
One other area you may be interested is school psychology, particularly if you are interested mainly in younger people with autism (ages 5-18, generally, those involved in the K-12 school system). School psychologists are trained to both provide direct care to children in K-12 schools as well as to conduct research; school psychology academic positions are also less competitive, as most school psychologists work in school districts. Of course, the research and practice that school psychologists do has to do with K-12 students’ functioning in schools - but that’s a pretty broad area, and there’s a lot to learn there especially in the areas of learning, cognition, and mental health. To be a researcher or academic in school psych, you’ll need a PhD from an APA-accredited program (a list can be found in the APA website). But if you are only interested in practicing in the schools, a specialist-level degree is all you need; a list can be found on the NASP website.
You can study autism from a variety of approaches within psychology (and neuroscience). The subfield only determines the approach you take, not the research questions. So developmental is one approach with a set of methods and theoretical framleworks; cognitive psychology is another, with a different set of methods and theoretical frameworks (overlapping, of course - psychology is the broad field - but still different). Clinical psychology is yet another approach (and clinical psychologists are also trained to diagnose and treat mental illness in addition to conducting and consuming research).
Also remember that PhD programs are pretty flexible and customizable. You could, for example, go to get a PhD in school psychology and do a lot of research with developmental psychologists. Or vice versa.
Here are some universities with great programs in developmental psychology. Mind you, though, that you’ll have to visit the faculty websites to see if there are people doing research in your area:
University of Minnesota (has some of the best child development people/research! Also has a great school psych program)
Penn State (great centers and research here, and also has a school psych program)
Michigan (they are strong in a variety of fields, developmental included)
Stanford (ditto)
Yale (ditto)
UIUC (ditto)
UCLA (ditto)
Cornell (lots of great early developmental theories came out of Cornell)
This site has a list: https://www.socialpsychology.org/ggradoth.htm#developmental
Here’s a list of school psychology programs. I’d take the rankings with a grain of salt, but the list is valuable: https://www.bestcounselingdegrees.net/best/doctoral-programs-school-psychology/
When you’re looking for school psych programs, keep in mind that school psychology is different from educational psychology. There’s a lot of overlap in research, but school psychology is about the educational behavioral, mental, and social needs of children in schools and prepares you to practice; educational psych is about the science of learning, and does not prepare you to practice.