She should. This sounds like a normal reaction to the immunization, indicating good immune response. No reason to avoid her booster at age 4.
No. Unless it's a very severe or life threatening reaction, it should not prevent your child from receiving another dose of it. It's often hard to figure out if the reaction was a coincidence or truly because of the vaccine. And remember, vaccines work by stimulating the immune system it's the immune response that causes the fever, so, it should reassure you that the vaccines working!