I am a primary school teacher in NSW, taught kindergarten for 3 year.

Judging on what you said, I would send her.

1. She is not too young. July 31st is the cut off and as Onyx said you dont just suddenly become ready for school when you turn a magic number. I have seen plenty of five/six year olds who seem less ready than 4/5 year olds. It is so dependent on the child that is why the option is there.

2. If she attended the orientation days and the school said that she seemed ready then go for it.

3. If the school has invited her to attend starting week 6 then they would be doing it because they think she will be fine. There is no gain for the school in having her start at this time (ie. numbers).

4. I wouldnt want her being at home 7 days a week being bored out of her brain (not suggesting you are boring- Just saying IYKWIM).

FWIW my birthday is mid June and I was 4 years old when I started. It was a non-issue. I was an above average student, well adjusted and had no issues with my age throughout school (I was too young to go to clubs in Year 12-but that is probably a good thing yeah?)
My older sister's birthday is the cut off date. Her pre-school advised my mum to send her or she will go insane. My sister never had any issues and has always been well beyond her years, socially, academically, mentally. So as I said, if they didnt want June/July birthdays they would have the cut off as April/May.

You use your judgement as well as the advice you have seeked from people who know your DD and are in the profession. HTH