If your DS is due to start school in Sept I assume you've already filled in the standard application form from the local authority? I think you will be finding out in a few weeks where he's been allocated a place?
The unit you're referring to? Again, do you have a specific one in mind? Have you visited it? If not, I suggest you do as soon as possible. I would also suggest visiting some specialist schools - if only to see what provision is out there.
All the specialist ASD units I know of (my DS is in one) require a DC to have an EHCP - or to be 'working towards one'. If your DS's nursery is recommending applying for an autism specific unit, I would strongly suggest you - or the nursery - apply for one now.
Legally, the whole process should take 20 weeks but local authorities rarely stick to those timeframes. It's not unheard of for the process to take around a year if you have to appeal.
Make sure the local authority stick to the timeframes - again there's info here on what to do if they don't.
Here's how to get started:
www.ipsea.org.uk/pages/category/education-health-and-care-plans
A good EHCP will contain details of your DS's needs and a list of targets/strategies on how to meet them so it's a really vital document that could see him through until he's 25.
As part of the process, your DS should see at the very least, an educational psychologist, a speech and language expert and an occupational therapist. They can recommend what type of support - and setting - your DS needs. Without those documents, it's going to be hard to argue for a place in a specialist provision. The nursery's evidence will also help.
When your DS was diagnosed, did the team say anything about what setting they felt he needed? Again, that will really help. If they didn't, can you contact them to discuss this?
One option could be - he might be able to stay at his nursery if you have to appeal. He could either start school during reception or even be educated out of year (ie start reception a year later).
I know the whole process can feel overwhelming but there organisations out there who can help - and some helpful and knowledgeable people here on these boards.