I had never thought of the mooshroom as "creepy" looking, in regards to eyes or anything. IMHO, it looks fine as is, and wouldn't see a reason for an art change. That said, I probably wouldn't even notice until after I read a changlist *shrugs* No support as I'd rather see other stuff done, nothing against this.
This is pretty much just an opinion-based suggestion. They could seem creepy to you, but an entire half of the world might think Mooshrooms are adorable as is. If an update suddenly made Mooshrooms have normal eyes, I wouldn't think to care, but I think the pure black eyes are an excellent touch to add how abnormal and unique the mob is.