As the baby is one month old please do not give even water from outside. It can cause infection and other concerns. Any oral remedy even a home remedy should be discussed with the doctor.

It is find probably the baby needs burping. Place on the shoulder and massage lightly the back to burp. You may also include jeera, ajwain water, garlic to avoid indigestion

If it is a little spit up then it's fairly common. If it is a lot of milk coming out then make sure you are burping baby well. If it is still persisting then you should see the doctor. If baby is vomiting for two or more consecutive feeds then baby should be checked.