You don't sound silly at all asking about christening and I hope I can help you get the ball rolling for your daughter.
My DD arranged her own christening into the Church of England when she went to university three years ago. In a way, she was following in my footsteps as I was christened into the C of E when I was 16 (my decision) and confirmed the day after. I have intermittently worshipped and taken communion ever since in Protestant and Catholic churches in the UK and mainland Europe, taking her with me since she was very small, and lighting candles with her to remember and talk about people close to us who have died. She is now an active and committed member of the international Protestant Church in the country where she is spending a year as part of her degree.
Your daughter is still a child and you are not christened so there are similarities and differences between our situations. In your shoes, I would look at the websites of local churches and talk to your daughter about what worship and other activities they offer for children. You will need to think a little bit about the different 'branches' of Christianity - principally (in the England) Church of England (Protestant and the established church, with the monarch as its head), Methodism (Protestant but non-conformist because it is not part of tge established church), and Catholicism (the church of Rome and the original Christian church).
Another consideration is about degrees of formality and informality - eg in the C of E following an order of service with the whole congregation versus children being taken aside for part of the service for an activity such as singing songs about Jesus and the bible, making seasonal items such as a crib or Christingle; a choir singing set pieces and also leading the singing of hymns, psalms and plainsong versus lots of singing to live music led by members of the congregation.
Then I would go with her to a Sunday service in the church or churches that your daughter and you think she would enjoy - two or three is probably enough. Most are at 10.30am and last for about an hour. Churches are always welcoming to newcomers and certainly don't ask if you are baptised or confirmed.
If you go to a service where Holy Communion is offered (in Protestant churches, the taking of bread and wine by members of the congregation in memory of Christ's sacrifice upon the cross, in Catholic churches usually just the bread), you can remain in your pew or take up the invitation to kneel alongside the communicants to receive a blessing, keeping your hands below the altar rail so the officiant knows not to offer you the bread and wine.
At the end of the service, when the vicar/minister is saying goodbye to people at the door or if there is the opportunity to stay for coffee, you can ask to have a word about baptism for your daughter and what preparation she will need to make.
Could you also ask around at school to see if there are families who attend local churches and could introduce you?
Your question about whether you need to be baptised for her to be baptised is an interesting one. I think it unlikely as you would be being asked to profess a faith which you don't have.
Please ask me more questions if you wish and I will do my best to answer 😊