You 'label' a parcel, not a person! Would you say that someone who has diabetes has a 'label'? A diagnosis of a condition can be beneficial in so many ways. It acts as a signpost to people working with the DC - and it can also help the DC themselves understand why they find some things challenging. There are recognised strategies and support that can be put in place at school and at home.
However, any support a DC needs at school/nursery is needs based rather than diagnosis-based - or should be anyway.
It can be very difficult to come to terms with the fact that a DC has additional needs. My DH cried when our DC was diagnosed with autism (even though it had been pretty clear for years). I think you can hold on to that small crumb of hope for as long as you can.
The thing about DC who have autism is that just like all other children, they do progress and change throughout their lives. It's just that it can take them longer to reach certain milestones. For example, my DS didn't talk until he was almost 4. However, even now although he has a reading age and vocabulary four years ahead of his chronological age, he uses spoken language in quite an 'usual' way and always will.
If/when your DS starts nursery, they should work with you to address any concerns you may have.
If you're worried about him settling in, I would look to start him sooner rather than later. It will be better for him to start socialising with his peers now before he starts school.
It's completely understandable and normal to worry about him. I would also warn you that where we live, there's a 3 year wait for an autism assessment and around a year for a SALT referral so you need to get the ball rolling as soon as possible. As others have said early intervention is so important.
My Ds is 14 now and I used to wake up in the night terrified about his future (I still do but that's another story!). He's thriving in his school now because he's got great support in place. He also knows what his triggers are and is starting to learn how to manage them. He knows about his diagnosis and that has been really important for his self-esteem.