I've never (until today!) written "levelheaded" and if I were to, I'd write it with a hyphen.Here's a useful link showing many single words that are often erroneously written as two separate words and vice versa . . . and some that can be written either way:
I think if we're all honest, we commonly get confused about some of these. For example, I often want to spell "high school" as one word.
Dictionary fight!
level-headed
1. calm and able to deal easily with difficult situations 2. calm and able to…
dictionary.cambridge.org