Despite at-will status, is it ever simply too soon to fire?

Q: My full-time salaried employee in Florida was hired four months ago and recently was assigned to a different job within the company. I provided her with a new job description and offer letter detailing compensation changes. She initialed the "employee at will" section and signed both. After all this, I feel that she is just not working out in this position. My question: Can I fire her at any time even though it's only been a month that she's been in this position? – HB, Florida