Teaser 2810: Almost a year apart

From The Sunday Times, 31st July 2016 [link]

Tomorrow’s date is 1st August 2016, which in the usual six-digit format is 01 08 16. This can be regarded as a “square” date since 10816 is a perfect square. No square date is followed by another square date exactly one year later, although some pairs of square dates are very nearly one year apart.

Which two square dates (in their six-digit format) come closest to being a year apart?