Based on experience with DSD, I think 4-4.5 is way too early. I'm from the US and was more than ready even with a summer birthday, but kindergarten there starts at age 5-6. I didn't realize what a difference there was until DSD started school.
Looking back, DSD was just confused during P1 and was not ready - not emotionally, especially not academically. At 4.5, she was still being dressed in the morning, couldn't/wouldn't zip up her own jacket, wasn't putting on her own shoes, wasn't wiping her bum properly, and wanted the adults to do every little thing for her (and several happy to do so, thus holding her back). She wasn't ready to read or do much with sums besides "2+2" either - she stayed on the same book band/ORT stage the entire school year. Constantly moaning that she wanted to go back to nursery and liked it better there.
Making much more academic progress now, though, so we're hoping that the "she'll just fly" wisdom is indeed correct. And socially, she is one of the most popular girls in class. Also one of the tallest and most athletic. So, she's right where she's meant to be in that sense.
It would be easier on DH and I if she was quick with her reading and sums - it is hard to fit in that much at-home learning support between picking her up from the childminder at 5:30/6:00 pm, feeding her tea and putting her to bed. But maybe if she was quick, she would learn to coast through school like I did, and really freak out when some of the material becomes finally, actually challenging.