It's a very bittersweet moment isn't it? When you finally hear those words from a professional.
When my DS was diagnosed, my DH cried at the appointment. It's perfectly understandable to feel knocked sideways, even for those people (like me) who had to fight and fight for a diagnosis.
Right up until I got the actual diagnosis I was thinking 'maybe he won't get one'.
Be kind to yourself and (I say this because this is what I do!) - try not to think too far into the future. I can sometimes go down the spiral (especially at 4am) of thinking: What will become of DS? Will he ever get a job/partner etc? But that way madness lies.
Your DD is still the same lovely, happy, funny girl she was yesterday. All that's changed is that she will have an explanation of why she finds certain things difficult. It will help her at school and to navigate the world better.
My DS is actually proud of having autism now. He refers to it as his 'super power'. He likes knowing that he's not 'neurotypical' and that he 'sees' the world in a different way.
Of course it's not all plain sailing and he has a lot of difficulties and challenges. These change over the years though, just like with any DC as they grow. You sound like a great parent who is doing their absolute best for their child.
Have you told your DD about her diagnosis? We told our Ds as soon as we came out of the appointment. I explained it in very basic terms and he started coming back with questions a few weeks later.
For me, I wanted to tell him straight away so he understood that it's nothing to be 'ashamed of' or frightened of. I understand there's no one right approach though.