I used to think is never be the parent who took their kids out of school for holidays etc, but having started them.in primary and seen how many do, and also how relaxed the primary curriculum is and how many days they have disrupted by things no more educational than a family day out / holiday, I have taken them out on odd days here and there, either for a weekend away, going or coming back from holiday just before or after the school holidays or theme park trip.
I don't think I've ever taken them out more than 2 days in a year though for things like that, none some years, and am avoiding it more carefully now daughter is in secondary school, as I do think she is more likely to struggle to catch up with 5 lessons a day. I'd also avoid it if they'd had a lot of time off sick that year. I don't care about 100% attendance awards though.
I'm not a fan of whole weeks off for holidays in term time as that seems a lot to miss,
Much harder to catch up on etc, and also leaves me struggling to fill /cover school holidays!
I probably wouldn't do it on her actual birthday though as I think that could set a bit of a precedence. But given to her as a birthday present and told this was the only day you could go so as a one off you have to miss school, I don't think will give her the wrong idea particularly. She's almost certainly seen classmates miss time for holidays by now. Loads do it in reception and of course the kids will talk about it when they get back!
I wouldn't lie about it - kids will tell and until term after she is 5 they can't really do anything anyway. Even then my area only fines once you get to 5 unauthorised days in a year, not even that since covid I don't think.
In my school there is a leave of absence form to fill in for planned absences and ive always done it and had a slips back saying unable to authorise, but no one has stopped us, said anything else, told us off etc! The one day I said something sheepish to the head as I handed it in the office, she laughed and said 'at least you are telling us. It's amazing how many dont or lie but we always know! It makes us laugh how people think their kids don't talk!'