This is a very reasonable and good question. The answer is not so easy. Here are the basic statistics. In children this age who develop wheezing in whom neither parent has asthma OR hay fever now or in their past, most of these children no longer have any asthma problem by the time they are 5 years of age. These are mostly nonallergic children who respond by wheezing to viral infections when they are young.
In children where they have a family history of allergy and/or asthma, the majority of these children are still wheezing at 5 and many continue to wheeze through childhood. It does not necessarily mean they will have severe asthma, only that they will have some wheezing with allergic or infectious exposures.
The reason your daughter may be a little different from the "usual" is the pneumonia you have described. This insult to the lungs may change the "usual" pattern in some way. It is difficult to predict what will happen in the next few years. It is possible she will wheeze with infections (not uncommon in allergic and nonallergic children). It is possible she will develop wheezing with exercise and other stresses. It is also possible none of this will occur. Your best bet is to work closely with your doctor to monitor the progress and deal with the course as it unfolds. Asthma is a very treatable illness in children.
It is not uncommon to have asthma in connection with an infection, such as a cold or virus, especially if it is a "bad" one. This does NOT necessarily mean that the patient will always have asthma. The course of asthma is really not all the predictable--some patients who have asthma in connection with infections do NOT have asthma any other time, while some do.
You are doing the right things by working with the doctor and observing your child & reporting anything of concern to the doctor so you can work together to keep your child as healthy as possible.
By the way, there are good medications that can control asthma well (with few or no side effects) and allow most folks to lead active & healthy lives. As an asthmatic myself & mom of two asthmatic teens & wife of an asthmatic, I have personal knowledge of the treatments available. We are NOT hampered in our activities by our asthma; it is well controlled and rarely ever troubles us.
Starion