Upvote:3
See Transporting animals as additional carry-on baggage in the cabin, especially "Specifications for the transport container":
"The maximum size is 55 x 40 x 23 cm (22 x 16 x 9 in).". The container has to go under the seat in front of you, so the dimensions really do matter. 23x15x16 is likely to be too tall to fit.