Change in routine? By all means, yes!
Way back in the old days, before Will was diagnosed and only around two years old, we knew something wasn't quite right. His language acquisition had stalled, he wasn't as interested in the outside world, didn't point to things, didn't flirt with waitresses at restaurants like he used to, and any myriad of other small, quiet changes. Nothing radical, just very small changes.
But we were still unaware. Just by accident, we had a very constantly changing environment. We moved to a new state across the country when he was fifteen months. We were building a house, so we lived in Grandma and Grandpa's house for almost a year while the new house was being built. We were constantly doing new things. Quite by accident, we were ALWAYS changing Will's routine.
I'm a real advocate of CHANGING THE ROUTINE. Do something new every day. Drive different routes to and from home. Don't let your child wear the same type of clothing every day. Don't let them eat the same thing. Mix it up. Make changes in routine THE ROUTINE! During this stage of life, my husband worked in an office by himself, so at lunch time he would pick Will and I up and we would go out to lunch probably three days out of the week. When we look back on this period we feel bad because we spent so much money doing this, but we also are convinced that this helped Will get used to new people, lots of noise, and changes in routine. We went somewhere new every day. As Will grew older, we used the restaurant experience to teach him social skills -- having to look at the waiter or waitress, ordering his own meal, and picking up on the occasions when the waiter or waitress was paying Will special attention because he was a cute little guy.
I don't know if this would work with all kids on the spectrum, but I think it is worth a try. In the beginning it could be painful [lots of crying from your child, lots of resistance] but ultimately it could make future changes in routine easier, and make the anxiety your child feels from changes in his future less and less as he/she gets used to new experiences.