Seconding Tony: from what I've read the logline MUST be one sentence - but it's always best to write something that's too long first and THEN cut it down into a shorter length. I also don't think you should supposed to include the genre in parentheses at the start - ideally we should be able to tell the genre from the logline alone WITHOUT having it explicitly stated. Similarly with the exact age of the character - maybe try: 'Her young son, Alex, contracts are rare disease and now she has to find a cure.' or 'Alex, her young son, contracts a rare disease and now she has to find a cure.' From that alone I would guess he's 9ish.
One guess: 'College professor Veronica McCabe must shut down a federal Disease Center and their nefarious animal testing in order to find the cure to save her young son.'