Request an EHCNA. Appeal if refused.
The first, relatively low, threshold you need to look at is that for an EHCNA. The only lawful tests are a) has or may have SEN, and b) may need special educational provision to be made via an EHCP.
You won’t have a finalised EHCP before the application deadline. With a few exceptions (including where it isn’t practicable for the LA to comply due to requesting information from the school over the summer holidays starting one week before they close and finishing one week before they reopen) the legal timescale is 20 weeks, not 26 weeks. Where the exceptions don’t apply, if LAs do not adhere to these timescales, parents don’t have to allow the LA to take over a year, they can take steps to force the LA to act, including via JR. It doesn’t matter if the EHCP is finalised after the normal application deadline, you should make a normal application but if an EHCP is issued the placement named in there will override the offer made via the normal application process.
Unfortunately, because some have to appeal, sometimes more than once, having an EHCP prior to the start of secondary school isn’t guaranteed.
DLA isn’t relevant. EHCPs are based on needs rather than diagnosis. They are also about more than academics, so being academically able doesn’t prevent DC from getting EHCPs. You can get EHCPs for DC who are still making expected progress in their learning. Many have to appeal because LAs like to act unlawfully, but it is still possible. You can get EHCPs even when the school doesn’t support the application. Again, some have to appeal but you shouldn’t let that put you off. It isn’t lawful for LAs to refuse because there has not been several APDR cycles. It is not part of the lawful test. It is a myth LAs and some schools like to perpetuate. And any decision now should consider the upcoming transition to secondary.
Grammar schools are still mainstream schools. They are selective mainstream schools. From your posts, DD would still need support in a grammar.
DD’s needs are not being met currently. She may be flying under the radar at school because she is academically able without behavioural concerns but, for a start, she has clear communication and interaction needs that are not being met.