It's kinda hard to tell, but all three members of the Warring Triad are in smaller versions of Dalamud in the Aetherchemical Research Facility. They just havn't been launched into orbit yet...

Dalamud itself is humongous. You can best see how large it is in the North Shroud. There's a huge curved piece of it lodged in the earth. Anther good places to see how big it is/was is in Eastern Thanalan at the Burning Wall. The pieces of it seem to indicate Dalamud was far wider then the bowl of the Dawn Throne. Dalamud was so big, people thought it was a small moon after all.

Tiamt would never have been contained in something like Dalamud. She is not a primal, which was what Dalamud was designed to contain. She could have been one of the beasts guarding it like Twintania was.