It is not easy to find a place that will rent you ...

It is not easy to find a place that will rent you kayak before sunrise,however, I found a Texas Rowing Center which opened at 6AM! While the sunrise occurred an hour after, I got at least 30 mins of paddling in darkness.
However, pay an attention - though you receive a headlight be careful of rowing botas - it is better to go to southern shore.

Hopefully it will help somebody - it took me quite a lot of time to find an appropriate place.