Can I be terminated from my job while under a doctors care

Maybe. You need to stay in close contact with human resources. Respond to all their requests immediately. Complete necessary paperwork timely. And aske them for extra time if you need it. The type of work you do, the size of the employer, and the hardship your absence might cause all play a role. There are no guarantees. If they discover something you did on the job which has nothing to do with your absence then they can take action on that also. Call them regularly and work with them toward a return date. Especially if you are at will which most employees are.