you see, rose, there's that anger again.
noone has defended the nursery worker.
everyone has said she handled it badly.
most have agreed that you should complain.
but at the same time, that you should think about what she has said.
because, in the experience of nearly every poster on the thread, nursery wokers do not raise concerns willy nilly.
your snide assertions that "she must have been on a course" and that she is over-keen to dx (which she has not attempted to do - your OP says you think she may be suggesting your ds is on the spectrum - not quite the same thing as her saying your ds has ASD, is it?)
noone has said that they think your ds has ASD.
ime, (and the experience of ohh, about 90% of the SN boards, I'd say) nursery tend to underplay concerns. they brush things aside which are total red flags. they completely do not know enough. which is why the worker is trying to suggest assessment. by someone who does know.
I too, am bemused as to why you would not apply for this. it takes months. and even then, it is usually not over in one appt. you are aske dot wait and see, and come back in 6 months.
you can gather all your evidence (either way) while you wait for the appt.
but it would be a shame to not apply, gather evidence that suggests your ds may need an assessment, and then find out you need to wait another 8 months or so, wouldn't it?