She got a period one week after the previous period

Yes, it comes under the same rulings as an ordinary menstrual period, because the basic principle is that the blood which comes out of a woman is menstrual blood (hayd) unless it becomes apparent that it is the blood of istihaadah (irregular non-menstrual vaginal bleeding). 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) was asked about a woman who started to bleed nine days after the previous period. He said: 

When the hayd (menstruation) comes, it is hayd, whether that was a long time or a short time after the previous period. If she menstruates, then becomes pure (i.e., her period ends), then five or six or ten days later she gets another period, then she should stop praying because it is hayd (menstruation). The same applies every time she become pure then the period come again – she must stop praying. 

Fatawa al-Mar’ah al-Muslimah, 1/79 

And Allah knows best.