If your post was focused on concerns that your child wasn't ready then my response would have been different but this desire to keep her off one day a week is selfish as it's all about your wants OP.
As a Reception teacher, I can tell you now that she will miss absolutely loads by being off one day every week (1/5 of learning time!). She won't just miss out academically, but socially too. Children who miss a lot of school and have patchy attendance do often struggle with friendships. Even if they themselves are well rounded socially, they do tend to get left out more if they're not always there as the others are so use to them not being around. The other children will have experiences they've not been a part of, making it harder for them to integrate:- "let's play that game we played yesterday!" (your child has no idea what that was) etc.
Key texts are usually covered for a week or more, so your child will always have gaps where work wasn't quite completed or finished. New phonics sounds will be introduced daily, so they'll miss a lot there. PE may only be taught on the day she misses, or that may be the only day Reception attend assembly or do baking or forest school. Maybe that will be their library day, or the day they do buddy reading with Year 6. There are so many things your child will miss through missing one day every week.
It's normal to feel emotional when your child starts school. It's not normal to keep them off for no other reason than it being what you want. You need to put her needs first. Family time is indeed still important but can still be achieved around school, like everyone else does. You know she'll have to go full time in January anyway, so there's no point delaying the inevitable just for one more term of daytime jollies during term time. All you'll achieve during that term is to single her out as being different, and cause her to miss out on lots of lovely experiences at school.
Your little girl is growing up. The fact she is looking forward to school is wonderful. Sometimes the best thing we can do for them is to learn to let go.
School are highly unlikely to be supportive of your choice, for all the reasons I've outlined. Just because you legally can keep them off until they're CSA, doesn't mean you should. Each case is different and, in this case, you are definitely thinking about what you want and not what is best for your child.