While children normally commence formal primary education before their 4th birthday (often at the start of the term in which their 5th birthday occurs, if not before), the provisions of Sections 7 and 8 of the Education Act 1996 (relating to compulsory education and parents' responsibilities in respect of it) don't take effect until the child's 5th birthday.
SATs, per se, only affect children in school years 2, 6 and 9. (There are no SATs for 4 or 5 year old children). Schools do, of course, make initial assessments of children's skills and abilities (so that they can measure progress) but that is not done through formal SATs.
When I was teaching I used to get driven mad by parents who took their children out of school during term time but, on this occasion, I'd recommend that you simply take your daughter on holiday anyway, because there's absolutely nothing the school can do about it.
Chris