Not all special/specialist schools cater for the same profile of needs. Not all have cohorts with significant learning disabilities, and not all are SEMH schools. For example, there are some SpLD schools admitting dyslexic pupils - although depending on what you mean by loud and lively, they may not admit.
I would look at all options within travelling distance. Special/specialist schools, ARPs/unit within MS, and MS. Within the MS options, I would investigate if any have a nurture or transition group (and if they do how long it runs for, some run only for Y7, some run right to Y11, and some in between). I would also ask about what non-academic options they offer in KS4. It sounds like a full GCSE timetable would be incredibly demotivating for DD unless something significant changes.
When you say a local unit, do you mean a unit within a mainstream? If so, they are mainstream placements, not part of a SS.
Personally, I would pursue an EHCP regardless. DD clearly needs more support whatever the placement.
If you are unsure why the school has suggested considering SS for secondary, ask them.
What I can say is the demands and expectations increase as DC move through secondary (and actually this applies as DC move through KS2 too). Academically, socially and behaviourally. If DD is struggling now with academics and with concentration/focus/sitting still, the gap is likely to widen as she gets older. For lots of children who struggle with English, they find those difficulties still over to many other subjects at secondary, even subjects like maths. That may well have a serious negative effect on DD’s MH.
What support is the school providing? Does DD use a laptop/tablet and assistive technology, including trying speech to text software? Difficult without an EHCP, but have they tried a scribe? For when DD does write, have they tried a writing slope? Does she have proper movement breaks or are they half hearted breaks? Have they tried a wobble cushion, a standing desk, rocking chair, resistance bands on chair legs, exercise pedals under the desk? Do they offer sensory circuits? What support with emotional regulation are they providing?
Has DD had a sensory OT assessment? It sounds like she is struggling with the sensory environment. That may well be worse at secondary.
Has DD had an EP assessment? What about a SALT assessment?