Can lessening my baby's dairy intake lessen her congestion?

No. In days past we used to recommend decreasing dairy to lessen nasal congestion. Now we know that this will not improve nasal congestion. Nasal saline sprays and suctioning can help relieve your baby's nasal congestion. Dairy sensitivity in infants typically presents with intestinal symptoms or rashes.
No. There has never been shown to be a connection between mucus and dairy intake.
No. Generally dairy products do not cause runny noses. I have seen, however, babies whose nasal congestion disappear when dairy is stopped. I am not aware of any tests for this problem other than withdrawal of dairy products and rechallenge.
No. Although the vast majority of infants with nasal congestion demonstrate no improvement when dairy products are eliminated, I have had experience with a small number of babies who have responded favorably when dairy is stopped. I am not aware of any valid research on the subject.
Yes. There have been some studies regarding proteins in certain milk increasing mucous production. This is not universal. I recommend extra fluids such as water and broth during periods of nasal congestion although milk can also be given.
No. Many people feel they have more mucus after eatting or drinking diary but there is no correlation with increased congestion from diary intake.
No. Some people have the idea that drinking milk makes a baby more congested. In my years of clinical experience, I have not noticed that a baby's congestion gets better or worse after drinking milk.
No. The quick answer "no" probably holds for most situations. But, in a subset of children, cow milk allergy is aggravated by the ingestion of dairy products prompting increased congestion. Parents perhaps notice the intake of milk can often trigger a "phlegm effect" in the back of their throat--probably driving the notion that dairy produces increased mucous. Yet a sip of water can easily clear this.