I know its off thread a bit but you really don't need a diagnosis to start getting support, i learnt the hard way. What you need is supporting evidence of challenging/ different behaviours. If there are social communication issues with literal language, poor eye contact, lack of interaction with peers (even though three is young for playing together) you can ask your GP/ health visitor/ family centre for a referral to speech and language.
They will then do an assessment and if they see any of the described behaviours in the assessment (be confident they will, they know what they're doing to assess children) they will probably offer you a six week block of therapy sessions and you get homework to do to encourage positive reactions.
Post this you may well get an in nursery report where the speech and language therapist assesses your DS with his peer group, discusses behaviour with his nursery and does a report. This report along with any initial speech and language assessment report are the very important start of evidence trail that will lead to ultimate diagnosis (if thats what is right for you down the line).
If there are any issues around your DS's mobility like week fingers, poor coordination, unusual running style, difficulty holding cutlery then ask your
GP for a referral to occupational therapy. They will assess and advise and produce you another evidence report - Dyspraxia is quite common amongst Autistic children and early intervention can make a massive difference in building fine motor skills pre school age (basically lots of playing lego and playdough works wonders on helping to have the strength to hold a pencil to learn basic mark making pre writing).
All these assessments help you learn lots about behaviour and triggers. We are quite big on sitting at the table as a family. DS1 used to lean on his elbow at the table, which my father found offensive. It turns out his dyspraxia means he has very very low muscle tone so his slightly lolling head is because he doesn't have the strength to hold it up. He needs to do a lot of exercise to maintain any muscle tone. Knowing that he wasn't being deliberately difficult meant we let the elbow thing go and it was a slight pressure of at mealtimes. I also started serving cut up meals so he only needed to use a fork, another pressure relieved. At 11, he can now cut soft foods with a knife but we do his meat. Actually his meat tends to be more processed or casseroled because he has a chewing/ swallowing complication we haven't quite got to the bottom off. He was born without a suckle reflex and had to be cup fed.
Diagnosis, particularly for high functioning Autism, appears to be an evidence gathering game. But all evidence of behaviours helps you to get support. So any reports you get you can take into school and get the Special Educational Needs Coordinator (SENCO) on your side to support your DS where needed.
Funding in England for special needs children has in my understanding fundamentally changed this year, in my opinion through the back door, it has been very significantly cut, with top up support only for the highest need children. Schools used to be able to get blocks of additional support for children but now the first approx 16 hours support each child receives has to be school not LEA funded. I fear discrimination against additional needs children could well become an issue in future years.