Can I be fired for going on short term disability?

Maybe. Did you request an accommodation because of your apparent disability? What did your doctor say? How long did you need to be absent from work? What date or approximate date did you inform your employer that you  would return? You will be collecting short term disability benefits correct? One year of service gives you protection to keep your job if you require up to 12 weeks of Family Medical Leave Act leave. Of course, your employer must employee at least 50 employees. But even if the above does not apply to you, you might be protected by the New York State Executive Law also called the New York State Human Rights Law. If an employer knows that you require an accommodation or should know that you need an accommodation (i.e which could include time off from work with an anticipated return date) which accommodation does not cause an undue hardship for your employer due to almost any medical condition which incapacitates you, it might have to provide such an accommodation to you. Your key issue may be whether you asked for an accommodation, when you planned on returning, and whether your employer engaged in an interactive process if it knew or should have known that you needed some type of accommodation. Best thing is to call some employment lawyers or view some videos on YouTube at Employment Law Reality Check which always suggest calling many employment lawyers. Legitimate,  nondiscriminatory reasons for terminating "at will" employees are OK. But your facts at least suggest that there may have been an improper motivation in terminating you. A skilled Employment Lawyer needs to ask you some tough questions. These are never slam dunk cases, even with strong facts. Speak with Employment Lawyers.