Since our baby was born we often quarrel. Is this normal, and how can we get through it?

It is normal and very common; lack of sleep, changing roles and hormones make couples more easily irritated. What matters is working as a team, not competing over who is more tired.
The Quran describes pregnancy and nursing as weakness upon weakness (Luqman 31:14), and tells us to decide matters concerning a child by mutual consent and consultation (al-Baqarah 2:233). The Prophet ﷺ helped with household work (Sahih al-Bukhari 676). Practical steps: take turns with night duties; accept help from family; lower housework standards for a while; find ten minutes a day to talk together; and avoid big decisions when exhausted. Husbands sometimes feel sidelined when the wife's attention is on the baby; say so gently, not angrily. If the mother seems very sad or anxious for more than two weeks, see a doctor. See Mental health.