My daughter stayed in mainstream with support. She eventually moved to a special school in her late teens. At least half of her peers and friends were schooled via special schools of one sort or another. I have often wondered whether she would have been happier in a special school throughout secondary. At one stage she wished she had too. With hindsight there was no right answer, and pros and cons on both sides.
Primary school, I think on balance is kinder to children with LD. It's an atmosphere with a lot of very little ones around, so that children who are delayed blend in more easily. And younger children are more accepting and more inclined to be inclusive. Most sadly lose some of that loveliness when thrown into secondary.
In your position I would fully explore the options for staying and thoroughly test the waters for a strong EHCP provision. My daughter was, by quite a margin, the most in need that the school had had for some years. So the school was very proactive on her behalf during the statementing process. They demanded, and were awarded, 25 hours 1:1 funding, plus further resources, transport and external support. Having a strong backbone to your initial EHCP will give you a stronger hand further down the line, when you do need to change schools. If it also gives you a workable result, so that your daughter can complete her primary in situ, then that's brilliant. But, even if you need to move before then, you will be better off with a robust EHCP statement to work from.
Good luck with finding a school to suit your daughter longer term. I think that could be a difficult decision as the ASD and LD combinations are so many and varied and complicated. That's another reason that I wouldn't rush to change schools immediately, if you can afford to take things more slowly.