This is a difficult question because it is in some respects unclear, as the comments register.
I assume you don't integrate the two notions : whatever is comic (laughter-making) is beautiful; and whatever is beautiful is comic. You are concerned, I take it, with the first bit: whatever is comic is beautiful.
The comedic and the beautiful
A comedy could be beautiful by virtue of its structure, its elegance of development, its language, or perhaps the perfection with which it is acted. None of these features would make it an enjoyable, happiness-making comedy, however. One might leave the theatre or turn off the television with a sense that one had seen or heard a beautiful play (by the above criteria) which comedically fell completely flat, something that evoked the aesthetic appreciation of beauty but raised not the ghost of a smile.
Equally, the merest slapstick, disorganised and mumbled with poor vocabulary, could make one split one's sides with laughter without one's having any grounds or inclination to call it 'beautiful'.
Notionem tesserae (bits of impressions)
I am not sure quite how to respond to your remark about everyone's being beautiful in an ideal world. Your main question is about the connexion between comedy (an art form) and beauty (an aesthetic attribute) and I have suggested that comedy and beauty are in this perspective pretty much independent of each other. But to take up the point : if a performer is beautiful, I might or might not feel happiness and joy in their presence. My aesthetic reaction may be more detached and contemplative. And I may feel happiness and joy in the presence of a person quite lacking in beauty of any kind.
These are lines of thought, fragments of ideas, triggered by your question rather than an answer. An answer would need a differently worded, more precise and focused, question to which to respond.
It has been fun responding, even so. So thanks.