The downside side is that with GDD you won't get ABA funded by LEA or LSA trained etc - without asd as part of diagnoses.
OP - my son has got global development delay, it will be probably changed to learning difficulty soon. He is very delayed in gross motor as well - for this OT programme has been invaluable. We do a lots of exercises incorporated into play activities to help him. We had to go private, the NHS OT was useless. So if you have the possibility, find private OT trained in sensory integration.
If your dd has SALT needs, this needs must be addressed and met - complain about the lack of provision.
The best way to stir the hornet's nests ( as it's clear her needs are mot being met) is to apply for statement of special educational needs, check out Ipsea website for this.
Apply yourself. Don't be put off - everybody will tell you she won't get it, she is not the worst off bla bla bla - don't listen. Even if LEA declines to assess your dd for statement, it will kickstart things, as school will want to look as that they are trying very hard and you'll be amazed how quickly they'll start reacting.
Also, if you are on low income you can get educational solicitor via legal aid - and take LEA to tribunal if they won't want to assess your dd.
Have a good read of Ipsea website - there is a lot of info including sample letters.
And good luck, I know how scary it is to start fighting for your child. Don't forget you fight for her, the school's priority is tight budget.