Welcome to what could be the start of a very long journey.
Firstly the good news is the school are concerned and are being proactive to do something about it. As you will soon learn one of the biggest battles we have are with schools, there is such a wide variation between what support you will get, some just do nothing, others are helpful, some implement statements really well and others even once you have a full statement you can still end up battling with them.
Throughout all of this YOU will be the key driver that will keep everything moving. Arrange the GP appointment, push hard to be referred to a peadiatrician and don't be fobbed off. the once with the paed ensure that they don't discharge whilst you have concerns. Need also to get the educational psycologist involved as well and get an assessment from them as well (easier said than done). between, you the school and the range of proffesionals that you come accross between you, you need to try and get to the bottom of what your daughters problems are. Once you know that then the right strategies/support can then be put in place.
Whilst this school may be willing to provide a 1:1 TA to support, generally alot of schools won't provide any significant resources to an individual child without a statement. Therefore whilst this school might provide the support she needs - will the next one? the statementing process is a long one - hit the jackpot and it can be done in 4 months, realistically 6 months, but if you fall at any of the hurdles associated with this then the road to a statement can be an awful lot longer. Therefore at some stage you will need to consider applying for one to ensure her needs are continually met at this school and the next. It only needs a change of head, a few cut back s, a different set of priorities and hey presto the support shes getting will disappear rather quickly.
Another word of warning - sometimes its easy to jump to the wrong diagnosis as to exactly what the specific issue is that is leading to SEN, a wide range of issues are spectrum disorders and its not always easy to place exactly where a child is as many symptoms of disorders overlap. Over the last few years I've convinced myself that it must be this or that and thinking weve solved it but never really do.
It sounds like you are heading in the right direction, and the fact you are even here is a huge start. it can be a rocky road, you will be exposed to a whole new world of stress, anger, frustration, confusion and just about every other emotion imaginable.
Keep on top of things, keep notes, don't go to any meetings/appoitments on your own - take someone with you - quite often so much gets thrown at you its hard to remember everything, be even more organised and take someone with you that can take notes for you!
But most of all - don't be fobbed off - stand your ground, make sure she sees who she needs to see. Whilst the school are being positive and on the case then make the most of this and try to work with them - what do they recommend that you do to help her? how will they communicate with you? once a term parents evening is not sufficient for SEN children, additonal meetings are needed and alot of us have daily home/school communication books which help to correspond between us about situations.
Good luck, you are not alone, this board has a wealth of information and experiences on it, sorry to have gone on for so long but just wanted to reassure you that we've all been there, had those moments and sometime just need a bit of hand holding to get through the complicated maze of SEN world. xx