Mmm … While a christening should be a celebration I don’t think of them as being a party.
I realise you say you’re not churchgoers (I’m an atheist and generally only visit churches for aesthetic reasons) but you do seem to be missing the point of such a ceremony!
Your daughter has asked if she can be formally welcomed into the ‘Christian family’.
First, think about who you might ask to be her godparents. People you love, respect and trust - who will commit to guiding her spiritually (and socially!) through her life. As she’s not a baby she may have an opinion herself - but you’ll have more wisdom and foresight. Choose people who’ll add to her life. I personally wouldn’t choose close family who are already active in her life - this is a good opportunity to broaden the circle of people invested in her well-being. Someone who’ll take her out for cocktails and maybe buy her a ball gown. Someone who’ll talk to her about books and art and take her to the theatre. Someone who’ll invite her on adventurous trips. Someone she can go to with troubles and worries …
Choose a church and speak to the vicar. They’ll tell you what the ceremony involves.
Invite godparents, family, (adults and children), family friends and a couple of your daughter’s closest friends (with their parents) to a genteel celebration after the ceremony. Everyone will wear ‘nice’ clothes, not party clothes! They may bring small significant gifts - books, or pearls, or Premium Bonds.
Be sure your daughter also signs the thank you cards you will send afterwards.
Ensure her lovely grandparents are given every opportunity to live up to their responsibilities. Sit back and congratulate yourself.