DLA is what you call a passport benefit and a very good place to start. The form is long and technical. You need to evidence your claim with reports etc and if you can get support to fill it in by the hospital or a social worker do.
A family social worker or family support worker is a really valuable person to have around when you're adjusting to lifes new direction. You can ask the council for an assessment of needs and may get allocated one.
If you get tax credits or are near the threshold you can add the disabled child/ severely disabled child element.
You can apply to your local council for a carers needs assessment for support for yourselves as things like childcare/ babysitting is more challenging with an additional needs child. They should also be able to reffer you for support looking at home adaptations. Finances are stretched everywhere at present but dont be tempted to undersell yourself or your families needs. Your need is there too.
Again with the local council you can ask for direct payments to enable you to buy services in for your DD to access peer equivalent activities like going out to different places like zoos and activity centres, even the cinema. Or can be used to provide a non parent escourt to attend clubs like rainbows as she grows up (its lovely to allow DC to be just DC sometimes rather than their ever present disability).
If your DD likes animals riding for the disabled are a fantastic organisation and they do carriage riding which can suit some more / very physically challenged people get involved in an activity. Waiting lists can be long depending on area so its a bit of a case of initial enquiries about everything at this stage.
We have a local disability partnership who are great for signposting and do things like radar keys so you can use the disabled toilets unchallenged.
There are quite a few charities you can apply to for grants for certain things. They're never fast but if you have big ticket purchases coming up its worth having a google and asking on the special needs boards.