You are legally entitled to file for joint and shared custody. The likelihood of success cannot be predicted, but, based on the facts stated in your question, it sounds like you would have a reasonable chance of getting shared custody.
Louisiana law favors shared custody arrangements. The court, if it comes to that, will try to determine what is in your son's best interest and rule accordingly. Your schedule should not prevent you from getting shared custody.
This response is not intended to create an attorney client relationship and is based on the limited information available at the time of the response. Before acting on anything stated or referenced in this response you should consult with an attorney of your choosing and go over the specific details of your legal circumstances.
You are likely to get joint custody. The chance to obtain shared custody is less likely considering the age of the child and your work schedule. You should probably seek joint custody with as much time as you can get now and allow the court to revisit the custody issue in 6 or 9 months to see if shared custody is feasible at that time.
Every situation is different and you should consult your own attorney to go over all the particular facts in your case. The answer given is only intended to provide general guidance regarding rights and responsibilities.
Sign up to receive a 5-part series of useful information and advice about child custody law.