Could I still have anemia if I eat meat?

Yes. There are many causes of anemia and deficiency of iron is only one of them. If you get enough iron and are anemic, you need a medical evaluation.
Of course.... Anemia is simply a red cell mass insufficient to meet the needs of the tissues without triggering compensatory mechanisms. A mathematical definition is a red cell mass that is more than 2 standard deviations below the mean for age and sex. There are many causes of anemia, that reflect either decreased production or increased losses. If this is an issue for you, you need to be evaluated by your dr.