In K we had a "reading practice" box that I would stock with material. She could choose anything from the box to read aloud to me. I usually let her choose, but sometimes I chose.
I wouldn't call it (or think of it as) required reading in K. Even with an advanced reader I would still consider it reading practice at that age.
But...
For your DD, I wouldn't do any of that, at least for the first half of the school year. She's going to be hearing a foreign language all day. Her little brain is going to be TIRED by the end of the day. I would let her read whatever she wants (within reason of course), and not push it. I think my goal for those first few months, or even the first year, would be to maintain the current English reading level and not worry about advancing it. An immersion school experience is completely different than a single language experience. The families over on the Bilingual Education board could probably give you some helpful advice and wisdom.