The above link is a good resource for checking the general under seat dimensions, and is the same info a reservations phone agent will reference. That being said, the dimensions do not accurately account for any IFE boxes and/or struts between the seats. That's why I then further suggest Airbus Aisle and Boeing Window for traveling with a pet carrier just based off of personal experience. If selecting contrary (or opposite) to that you might have an issue with the length of the carrier due to struts, IFE, or a protruding console.

The height of the carrier can be a pain on any aircraft (well, except the 717s and former MD88s). If you'll notice the max height dimensions for F on an A321 is listed at 10.5". Most pet carriers are around 11" in height, with 18x11x11 being the most common on the market. If soft sided, these are easy to squish down somewhat to make them fit. On the AA website it actually specifically says this is an allowed practice, and DL does not. I once had a phone agent refuse to book my pet with an 11" high carrier due to a 10.5" limit. I called back and the second agent happily did. I've now gotten to where I will fudge the dimensions somewhat when booking just to avoid agent issues if they ask specifics. For an 18x11x11 carrier I will now say something like 17x10x10 just to avoid this. Or, most recently, the agent asked "Is the carrier 18x11x11 or smaller?" To which I replied "yes" and was no issue. Just FYI depending on how strict of an agent you might get.

I would not recommend anything bigger than 18x11x11 on any aircraft. If it's feasible to have a companion travel with you, I highly recommend that for the ability to move the carrier to the adjoining seat if it would fit better, and/or possibly in the middle between both seats. We've gotten to where if we take our pet, both of us travel with her. It makes it easier on having options to stow the carrier, and also doesn't mean a seat mate would be surprised to sit down next to a pet in F. (Though I've travelled solo with our pet before, and only once had someone make a remark).

Once the ticket/PNR is issued, use pnr.sh to verify the agent listed PETC correctly as an SSR for each segment. And with any schedule changes, make sure this sticks to the new flight.

One last tip, I highly suggest a thermal pack you can fill with ice from a fast food place in the airport. Having that in the carrier, along with a portable battery operated fan does wonders for keeping our Bichon Frise cool.