The thing is, even if you do get referred and do get an autism diagnosis, there may not be any practical intervention beyond a bit of paper at this stage. You will probably just be given the details of NAS etc, books to read, generic strategies which could probably be found online, or from your SIL even.
Nursery should be providing him with support whether he has a diagnosis or not, or pressing for an EHCP if they think he is in serious need of assessment by a professional. And YOU may be brilliant at intervening if you use autism-friendly strategies, most of those strategies would work for neurotypical and children with other needs, so you have nothing to lose.
Explaining things before you do them. Allowing for sensory needs. Investigating sleep problems via GP, possibility of melatonin, whether he has autism or not. Sensory "diet" (google, it is not about food) Another parent on this forum just ordered PECs cards for a four year old and that helped her with her son. Pushchair even if he is 4, rather than expecting him to walk. Allowing for possible hypermobility and pain in joints, might make him refuse to sleep, or play up when out and about. Later development re: toileting might mean you have to make allowances for accidents/soiling, he will get there though, don't despair.
Lots of books might help you more than a generic parenting course, try Out of Synch Child, How To Talk So kids Will Listen by Faber and Mazlish, Explosive child by Ross Greene, Guide to Asperger's Ron Attwood.
My son was not diagnosed until he was 8. I had no NHS help up till then and I think all our interventions (which were good ones mostly) were home grown and just happened because they worked. Sometimes we got it wrong, and I wish we had known now what the problem was and maybe it would have been a bit easier, but I'm just saying this to reassure you that ifyou think there is a problem, you personally will probably be the one finding solutions rather than the NHS and their impaired referral system!!! (got turned down twice, before diagnosis, letter from school helped massively to get final referral, and even then not diagnosed for a year after that)
and the other thing...find a support group for parents with special needs children it is really a life saver to talk to other parents and the information sharing too as well as the emotional support.