FWIW her school emphasizes self-expression through writing and journals (they're a magnet and this is their philosophy). So when they are journaling they are able to write freely without correction (according to the teacher this is when dd is getting frustrated). And there is a separate instruction time for the correct formation of the letters of the alphabet.
This was the philosophy at our kids' early elementary school also, but the kids were allowed to draw and illustrate as part of their journaling when they were in K-1, and with some teachers they were allowed to type by 2nd grade while in class during journaling/creative writing time. Perhaps you could suggest something like this, or scribing, for the short term until you can see if her handwriting catches up with a little extra work?
I'd also give cursive a try if she's interested in it - one of the schools that our older dd went to for summer school when she was having difficulty with reading purposely taught cursive first before printing and it worked well for their students. My youngest dd has always liked to create stories but struggled with handwriting... anyway, her school introduces cursive in 2nd grade, and she's loving it - for her, cursive is much easier and quicker than printing. So if your dd is interested in it, I'd go ahead and teach her cursive. Another option to consider is the scripts that are semi-in-between printing and cursive. I can't remember the name of what it's called! But we considered it for awhile for our dysgraphic ds, and there are a few different scripts out there - some of which you can find directions for for free online.
Best wishes,
polarbear