Have you had a referral for a "sensory diet"? They have specially trained NHS staff who look through what your child will/can eat, and then work out a balanced meal plan and suggest other foods kids with similar ranges eat so you can try to expand it a bit. Your paed should have suggested it but if they didn't, and you've not had a referral, ask?
DS will eat more widely when relaxed. His range contracts when stressed. At one point all he would eat was plain boiled pasta and some simple fruit; now, he will eat plain homemade pizza, homemade chicken nuggets, a particular form of chicken curry (so bland it barely qualifies!) baked fish, fish fingers, baked beans if in a very calm mood, scrambled eggs if same, very plain cheap ham if the bread is white and crusts off cut into fingers. He also eats most fruits, and ice cream. Will tolerate peas and sweetcorn and raw carrots, again if calm. He likes bland - so white bread, mashed potato, vanilla cake, vanilla ice cream. Hates chocolate cake. He can't even be in a room with a chopped capsicum pepper or a naice olive (deli kind, in oil - can handle the cheap in brine ones in his presence as they apparently are scentless to him) as the smell overwhelms him.
I'd say that's very young for a diagnosis... where I live they won't usually accept them until kids are around 7 (because there's so much development up to that age). If they are considering a disagnosis, your child must be very extreme.
DS was diagnosed at 5. He's not extreme; in fact in many ways he's high functioning. Strong social interest, unimpaired emotional empathy, immensely loving and affectionate, and exceedingly academic. But he's very plainly and apparently autistic to anyone with expertise in the area. Early intervention is essential for good outcomes and a diagnosis is usually needed to unlock that. DS was a mess before he had his diagnosis, and the targeted interventions have made his life a lot easier. We are lucky, I think, in that there are several autistic people in the family so we knew what we were looking at, and the HCP knew that the genetic factors made it the likeliest cause of his fairly profound social and emotional difficulties. He needs a lot of scaffolding and support and understanding to cope with his life, but with all of that in place he is thriving at the moment.
I think the "not till 7" thing for autism is very outdated - certainly it's seen as such here, where all the thrust is to identify and support early. Suitable for dyslexia, etc., sure, but autism in the early years is so subject to support making a long term difference to outcomes that it isn't sensible to cut any child off from that support with an arbitrary date.