It might be asthma. DD started with random coughing at around 3.5 yrs (it is like an irritating cough with no cold/runny nose) and it came and went and after 12 months or so it always turned into bronchitis. Doctor diagnosed viral-induced asthma and now if we give ventolin at first sign of cough we can avoid going down the bronchitis path (that's only been the last 6 months so not sure what next winter will bring which is her worst season for cough/asthma). Seems my DS has it too as random cough has started for him and a couple of puffs of ventolin helps. Definitely ask your GP if your worried.

Also like calluna said cutting back on dairy can help, we noticed a big difference in DD by cutting back milk and yoghurt.