What's it called when someone thinks something's cute?
The short intake of breath is called a gasp. In that sentence, TJ gasped, "Aww! You two are so perfect!"
You could also say TJ was fawning over the cute couple.
Though Cameron's suggestion of fawning is particularly good, this action could also be described as gushing:
to make an effusive display of affection or enthusiasm
"Aww! You two are so perfect!" Tj gushed.
[Merriam-Webster]