[Chess 960] Is it possible to castle here?

In chess 960: I would be obliged if someone could tell me, what if any are the legal castling options with this kind of arrangement. Is castling merely impossible with some starting piece arrangements, or is these a strange way to do it in a circumstance like this?

Neither of these rooks have moved, and the K is on his starting square.

From what I can decipher, castling should be legal if I move Qd1, by connecting with Re, but what is the position afterward, if I do this?! Further, the Chess 960 rules state:

The king must be between the rooks to maintain the ability to castle both ways.

(emphasis, mine)

This implies that I can somehow castle Q side with Rb, but the game did not start with any space between them. How does that work? Does Rb simply transpose to Rc, despite no intervening space?

yes, you should be able to castle if you move the queen, you can try it in the analisis of your game.

in that case the rook will move  to d1 and the king will remain in c1

Thank you.