Many times it seems to help the child if you reaffirm what they are feeling instead of saying, "you don't have to be scared..." I'm not saying you are saying that, but many people want to tell children, "You're okay" when in truth, the child is feeling anything but "Ok." Explain to her that everyone feels anxious and that there are many new things in her life. Tell her, "I know this is hard...but you can do it." Encouraging your child to be brave and independent while providing the tools and strategies to help her with this transition will be very important.

Perhaps giving her some pictures of her family to take to school might help. A picture schedule could be extremely useful, that way she will know what is happening and when she'll be going home. There is a good book out about "Managing Anxiety in Children with Autism" that might help. Autism and anxiety seem to often go together. Perhaps offering her some calming sensory input before leaving might help her feel better able to cope with going to school. Or perhaps a sensory diet throughout the day might help manage her anxiety? Be sure to show her and talk to her throughout the day about ways you handle anxiety. Point out other children in distress and explain how they handle their upsets. You will want to model numerous times how to handle anxiety. Perhaps writing down with an accompanying picture three of her favorite activities that are calming and then practicing with her on choosing an activity when she is upset might help. Hope this advice helps!

Perhaps introduce a fun new toy/activity that might keep her distracted enough so you could sneak off into another room nearby. It sounds like the clingy thing is a new behavior most likely due to the move (we had the same thing). I bet with enough time and reassurance, she'll get her confidence back. The picture schedule is a good idea too. My son uses one at school and will also ask for one at home (we'll write words on a sheet of paper since he can read).

Try a picture schedule. That helps with anxiety about new things.

It's always hard with changes, but take it one day at a time. Keep letting her know she's safe. Do as much as you can to keep her routines on schedule and keep her comfortable and hopefully she'll calm down and relax soon. Maybe additional therapy to help her through the transition?

It sounds like she may feel like there is a possibility that while she is at school, you will move away without her. If all the boxes have not been unpacked from your move, maybe you could let her stay home with you a couple days, to help you finish unpacking. That way, she will know you aren't going to move in the near future.
Then, I would take pictures of her day, especially pictures of her being picked up and arriving home to or with you. Have her help you write the captions under the pictures, reaffirming the idea that you will be there when she gets home.
If she has a special stuffed animal or doll, allow her to take it with her to school. Once you get there, talk to her "friend" telling it how much you need it to take care of your daughter until she comes home that day. Telling it to make sure your daughter doesn't get scared that day.