What you're describing here is really familiar to parents of children with Autism (not that I'm suggesting in the slightest that your child has it) because it's a response to being in an overwhelming environment.
Nursery, especially in the first few months, can be a challenging environment for any child. The constant social interaction, trying to read body language and predict responses, the effort of remembering rules and worrying about what may happen if you break them, greatly increased sensory input and a requirement to regulate and conceal your own emotional responses can be massively stressful and utterly mentally exhausting for a child. She can't just climb on your knee for a cuddle and a bit of down time while she's there so there is no respite for her just now.
That stress has to come out somehow. A well behaved child who cannot let it out in the nursery environment has to save it up and may well let it out over the next day or so at home. She may also be spending the next couple of days processing some of the events she's seen or experienced and be experiencing some of that stress again. She might explore those events through her play with small world toys or dolls when that is happening.
Because your DD is NT, she will soon learn the social skills and coping strategies she needs to get her through the day and, as she builds relationships with the staff, she will find ways of getting short bursts of respite, cuddles, stories, one to one activities and these times will relieve the stress for her.
This isn't her bringing home bad behaviour she's seen. This is her processing and expressing her emotions about her experiences and the challenges she faces in nursery. She still needs to know when her behaviour isn't acceptable but you can also help by making fewer demands on her at this time, having quite a predictable routine without too much sensory input or too many social demands, i.e. quieter times at home with just close family doing regular activities so she knows what's coming next.
It does take children a long time to truly settle into early years settings but it will get better as she begins to feel more relaxed there.