Nursery schools in Doha have increased over the years, with many more expatriate community run nurseries with English as their primary language being opened.  Although not all nursery teachers are qualified, and some nurseries not registered with the Ministry of Education, they are still normally taught at very good standards.
There is not normally a waiting list, so it should be relevantly easy for your child to be accepted.
Nursery opening hours are between 7am and 1pm, and some will stay open until 3:30pm or later.
 
Pre-schools are attached to primary schools, and take children from age 3 years old.  In contrast to the nurseries many good, pre-schools will have a waiting list.  It will therefore be necessary for you to complete an application form beforehand.
The added guarantee however, is that the teachers will most definitely have professional qualifications.