Is it possible my daughter has asthma?

I have a daughter who is a year old and she's very active but I've been noticing that when she's playing, crawling and waddling around a bit, she begins to start breathing heavily and turning red. Also now at night she starts coughing in her sleep and struggling for breath. The doctor says it has more to do with the fact that she gets all worked up and then she just has very small lungs. Are these warning signs for asthma?