Yikes I'm going to disagree !!! You mentioned you were trained in autism and had done extensive testing ? To my way if thinking unless dkp sent her to your Dayhome because of your experience then you had a right to screen her but other than that I do not agree with her being tested.
I know you would notice the behaviours and I think if you were asked you could fully go into it but it seems like they are not interested in you diagnosing their child . I am a mom with experience (25 yrs) of child care I have a dcg right now who I totally suspect has autism . She try's to hurt herself as well . My friend works with special needs and we have discussed her similar behaviour but I would never tell the parents I suspected it. Of course I'm not qualified to do so which I can imagine is hard for you given your knowledge !!! But I still don't think you should broach the subject unless it is brought up to you by parents . My dcg is leaving because I told dcp I am not comfortable with the self hurting and it was awkward because we all knew there's a problem but obviously they are not ready to admit it let alone get help ! Sad ? Yes !!!!! But I feel not my business !!