I urge you to have her evaluated by a developmental pediatrician. Her actions could just be quirky but you've described several different ones that can be indicative of autism or other developmental disorders.
My grandson, who is now 7, was recently tentatively diagnosed with being somewhere on the autism spectrum. He started having speech therapy thru the school district when he was 2 1/2 and is still unable to speak clearly enough for most people to understand him. He was diagnosed with apraxia of speech. He's been in the school system ever since. He's also very angry which caused the school district people to suggest he had ODD, opposition defiant disorder. Maybe he has that too but treating the ODD disorder has not changed his behavior at school, tho it has at home.
Developmental disorders are very complicated and the field is new. It's always best to get help as early as possible. I suggest it's also best to get an assessment so that disorders can be eliminated as a cause of behavior so that you don't continue to be concerned.
The school district is mandated by federal law to provide, without charge, diagnosis and treatment for any disorder that will negatively impact the ability to learn in school. They start evaluations and services as young as newborn.
My daughter and her husband at the time decided to wait and see about their son's lack of speech. It's possible that if he'd started speech therapy sooner he'd have better mastered speech by now. At 7 he's entering special education 2nd grade primarily because although he can now say many words clearly and speak in sentences part of the time he's not able to express ideas, concepts, feelings adequately in words. He's prone to temper tantrums. Although he's intelligent he's behind developmentally.
We just learned that developmental pediatricians exist and wish that we'd taken him to one many years ago. You are on the right track, having gotten your daughter started in speech therapy and motor skill development early. My grandson would probably be further along if he'd started speech, occupational and physical therapy sooner.
When you said she is in therapy my first question is what do her therapists say? My second thought was, that although my grandson has been seeing therapists for several years they have not been thorough in their evaluation. The school district does not employ a developmental pediatrician. They are short on funds and are unable to be as thorough as some children apparently need to have them be. The field is so specialized that a speech therapist, especially a young one with little experience as my grandson's have been, would easily miss other aspects of behavior.
My grandson seemed normal as to behavior during the "terrible twos and threes." But his behavior didn't change and in fact worsened as he got older. He does have ritualized behavior that didn't seem all that serious when he was 2 and 3 and learning about his world. Some of it is inappropriate at 6 and 7. Two and three year olds engage in a lot of parallel play. My grandson still prefers to play along side other children but by himself. He likes to have other children around and will interact with them but only if they do what he wants to do. If they don't want to play tag he just runs off by himself, for example. He asks me to play cards with him which means each of us line up our cards across from each other. Once all of our cards are lined up we pick them up and start over. We may use a different arrangement but playing cards is just laying cards down and picking them up again.
You can learn much about developmental disorders and autism on the Internet. The criteria used when making a diagnosis is outlined in the professional book, DSM, or Diagnostic and Statistical Manual which is arranged by diagnosis. You can read parts of it at a time on the Internet when you google the possible diagnosis.
I wish I'd spent less time trying to learn about various diagnosis and spent more time encouraging my daughter to get a professional diagnosis separate from the ones made by the school district. An early diagnosis creates a better possibility of making life for your child more "normal." You also need to know now so that if she doesn't need further help you can relax or if she does you can expend your energy on helping her rather than worrying about her.