You did absolutely nothing wrong in the store. I would advise you to bring along a small quilt for next time to put in the cart with your daughter because shopping carts can be very germy and disgusting. (Think of all those strange hands touching the cart before you got it.) Regarding the marriage -- yes, you and Justin should go down to city hall and get married. It only takes a little while and it offers you a lot of legal protection in the future if things should not work out between you two. A lot of people believe that you need to have some huge elaborate wedding ceremony but that isn't the case. Regarding the smoking -- making sure that your baby was in the air conditioning was a good move. However, you and Justin both should try to quit smoking for your daughter's sake as well as for your own. Even if you don't smoke around her and change your clothes, those toxins are still on your person. Additionally, children of smokers are at greater risk for developing childhood asthma.
Just my two cents worth of advice since you asked.
Finally, don't let people like that woman at the store get you down. There will always be people who gain pleasure from sticking their noses into the business of other people.