I think of this sort of cot as a small, light, mobile bed that can be wheeled in or out as needed, not a baby's cot. I was offered one once when I stayed in hospital with my daughter, so I could sleep beside her.
Going back to the cot discussion, here's an example I ran across last night in one of my favorite childhood books, The Crystal Tree
, by Jennie D. Lindquist, published 1959 but set about 1910. Helga is just about to turn 8, and her older sister Sigrid is moving to her own room:
"And," said Helga, "I'm not going to sleep in that little baby cot anymore. I'm going to sleep in the big bed with Elsa. Goodbye, cot! We're going to take it right out of the room and put a long table there instead. Elsa and I will each have half the table, with a chair each, so that it will be like two desks."
"Like boarding school, I think," said Elsa.
However, I can't be sure whether Helga's italics means that the cot was an actual baby crib (Ours, which we also contrasted with a "big bed," was plenty long enough for a 7-year-old, though by that age kids climbed over the bars on their own), or the kind of cot Mary's talking about, since in the next sentence we learn that Sigrid will be using a "bigger cot."