The proposal was 100% in character. Kimishima is a pure airhead, so she would always talk without thinking. Takaomi has loved Kimishima from the beginning, but had even managed to live feeling down after getting shot down by Kimishima, due to a misunderstanding. So, it makes perfect sense Kimishima would reveal her wish so haphazardly, whereas it also makes sense Takaomi wouldn't want to miss the chance when it's utterly clear he has got the opportunity. Due to his reserved personality he would have, no doubt, waited a whole lot longer otherwise. However, he would definitely not want to risk losing Sara again.
Btw, what's cheese lasagne? Cheese is a core part of lasagne anyway. There can't be lasagne without cheese, so what's cheese lasagne, then?