Walking into a detention facility with an active warrant is one of the worst decisions a person can make, and it will not end well.
Every visitor to a correctional facility goes through a background check and identity verification before they are admitted. That process flags active warrants. If the girlfriend shows up at the visiting room with an outstanding warrant, she will be detained on the spot. The facility will hold her until the issuing jurisdiction sends someone to pick her up. The visit does not happen, the baby does not see its father, and she leaves in handcuffs instead of walking back out the door.
It does not matter that she is bringing an infant. It does not matter that her warrant may be for something minor. Facilities are not in the business of making exceptions for people with active warrants who voluntarily walk through their doors.
The only sensible path here is for her to resolve the warrant before attempting any visit. Depending on what the warrant is for, an attorney can often arrange a voluntary surrender on favorable terms, which is a far better outcome than getting picked up at a prison visiting room. Some minor warrants can be cleared with a court appearance and a fine.
Until that warrant is taken care of, she should not set foot near any law enforcement facility. After it is resolved, she can go through the standard visitor approval process and bring the child to visit.