Hello
My DS has poor fine motor skills and in fact I would say this is the key 'special need' for him, along with listening/concentration skills. He has been having OT this term and come on in leaps and bounds, but at 3-4 was worse than your DS.
To be honest your DS sounds similar to a lot of boys his age, regardless of ASD/NT. Bear in mind that boys in general often have poorer fine motor skills than girls - partly because that skill simply doesn't develop as early in boys (if you have read 'Raising Boys' the author goes into the difference in brain development between boys and girls in the early years), and partly because they're less interested and would often (though by no means always) run about rather than draw a picture, so get less practice.
So rule one - do NOT compare your DS to any girl of his age. Even if both children are NT and developmentally 'typical', a girl will most likely be about a year ahead in terms of fine motor stuff anyway. I go in to DS's school once a week to help out, and most of the boys seem far less developed than the girls in terms of fine motor stuff, even if they're academically stronger.
NT girls often learn dressing type skills earlier too - they're often more interested in what they wear for a start, and also if you think about it a lot of 'girlie' clothes (pretty cardigans, tops etc) have far more buttons than typical 'boy' tops like short or long sleeved T shirts, so again, more opportunities to practice. Boys can be flipping lazy! But also bear in mind that OTs do not look for children to be able to fasten/unfasten buttons until they are 6 (so DS's OT told me).
My DS started school aged 4 and 2 months, at which point he had no concept of holding a pencil correctly (would grasp it awkwardly, like a 1 or 2 year old might do) and could only just about copy a circle or a cross but not really, if I'm honest. He'd do anything to avoid sitting down at a table to try drawing or writing. He could not do up buttons or zips either and scissors were a complete no-no. Dressing/undressing was hit and miss dependent on his mood.
Fast forward a year, after one year of reception, regular OT practice internally within school and 5 sessions of external OT, and it's a very different story. DS is now holding pencil correctly, can write his name, virtually every letter in the alphabet, can write sentences with guidance, can do both buttons and zips (fastening and unfastening), dresses and undresses with no help, including shoes/socks, and is mastering knife and fork skills. The difference in him after 12 months is amazing - in fact only in writing it all down now have I really realised far he's come, bless him.
The only skills I would say he is still really awkward in are scissor skills and drawing. His scissor grip is now good but he's still awkward when actually attempting to cut (very noticeable in comparison to peers at school), and drawing wise he's simply not that interested so does as little of it as he can get away with. So his drawing skills still seem very immature compared to others, both boys and girls. On the other hand, he adores Lego, and is confidently assembling models aimed at 5-12 or 7-12 year olds with minimal assistance. Whereas one of the little girls his age who we see regularly can draw or write beautifully, but cannot even begin to assemble the tiny lego bricks so beloved by DS!
I think it is too early to start worrying about your DS's fine motor skills to be honest, but no harm in encouraging scribbing/cutting practice whenever you can. Don't panic if he refuses though. And bear in mind that even if, like my DS, it does become more of an issue if he approaches school age, it's amazing what a bit of concentrated OT can do.