Hi! I took a look at the carrier you linked to and I think it looks good, but it will be dependent on the size of your cat. The description states that it's for cats up to 17lbs, so if your cat is pushing that size it might be a bit uncomfortable.

I have this carrier for my Maine Coons: https://www.amazon.com/dp/B087WSHGKW/ref=cm_sw_r_cp_apa_glt_fabc_YVD8AGWQFNVN2EWTSSTX?_encoding=UTF8&psc=1

I think it is airline approved for under the seat dimensions. My cats really like it- it has an expandable front to give them a little more space when I can and they like being able to look fully out the front bubble window. It an accommodate a cat up to 20lbs so it's perfect for my cats.

The only down side is that it doesn't have as many bells and whistles as the one you got- primarily the fan- and sometimes my cats get too hot in it. I additionally got an attachable fan https://www.amazon.com/dp/B07V5TX443/ref=cm_sw_r_cp_apa_glt_fabc_9B1DJ3ZR4EED9RDJMAKE?_encoding=UTF8&psc=1 and I always keep a couple frozen packs on hand that I out in there with them if it seems like they are getting warm. I would recommend keeping the frozen packs with you if possible no matter which carrier you choose because when cats get nervous their body temp rises and if it's warm on the plane they could become uncomfortable in the carrier.