If DD is tired then homeschooling is not a bad plan for a while. It will give you a chance to observe what is going on re fatigue and also academics. Before you do that though, can she have a week off so you can gauge better what is going on? I am not sure if you have enough information to know exactly where you are yet.
She could be 'sick' for a week while you assess if she is just tired. A physical check up might not hurt either. Growth spurts can wipe my DD out as do minor viral infections. Iron deficiency can be an issue in growing children for example. Lots of reasons to be tired.
Have a longer chat to the teacher too. Are the physical demands of the day a problem eg writing tasks? Is it the increase in EF demands? Or is she just developing normally but a bit wiped out by the daily routine? How is she placed relative to her peers?
You mentioned academic struggles but is that because she is tired or the reason she is tired? Can be a bit hard to tease out. The additional psychoeducational testing will help but all the more reason to have a bit of time off before then so she is not fatigued for the assessment.
If she is developing normally but exhausted by the day then keep her home for the rest of the year and let her grow and get stronger. Practise some writing and reading if desired and re-evaluate her progress later in the year with a view to K or first grade as appropriate.
You can explain that she is very young and she is growing and that takes more energy for some kids than others so time at home is important so she can rest and grow. She can do academics if and when she is happy to do so and she will learn with you while her body catches up with her brain.
It sounds like you have a good school to work with and I am sure they would be happy to keep helping you plan a strategy that works best.
