Ds2 was a delightful child(to me) but I would say the signs that he would go on to develop ASD, or had always had it were:
impatience eg: with food he didn't like the texture of, even when hungry
easily frustrated/bored/very lively
difficulty with textures
difficulty settling to sleep initially
He was hard work in a way because he spat things out all the time and screamed with frustration when he didn't get the chance to go out and see the world aged about 1 and half. Also he needed our constant attention and feedback. We gave it to him, but I am now realising maybe it was hard work, and that not all toddlers were so demanding...
The sensory processing stuff is important because a child with ASD gets overwhelmed by the noise and sensations around them. For example Ds couldn't manage a full day in Reception, and did mornings only for first year until he was over 5. When he couldn't cope he would go berserk, making loads of noise, running around like a maniac, crying. His desire for calm provoked the opposite response from his system. He needed lots of opportunity to release physical energy (park, climbing, rolling around) and very poor fine motor skills when he was little. But not so that you would notice if you were a HV. His communication was excellent, as was his speech, apart from a bit of dribbling. He loved chatting to people but he was obsessively interested in toys and played few imaginative games with them, more repeating a story he had heard already, or arranging them in towers, or lines.
I wonder whether your little girl is finding nursery life a bit overwhelming and that is why she is lashing out? Whether it is ASD or not, that might be worth seeing whether it improved things to see whether she needed more time in quiet setting 1:1. Ds loved things to be calm although as I say he was very lively and emotional. He benefited a lot from singing, and climbing, and dancing, and playing with his sister.