My one year old just had the mucus stuff coming from her eyes at the end of last week. It was the end of a week of cold symptoms and then discharge from the eye. I just made sure I wiped it out with a clean tissue or washcloth and made sure I washed my hands after. I made sure I was on top of the nose wiping, so none of the snot went into her eyes inadvertently.
I just kept up the cleaning for the three days that the discharge was coming and then it cleared itself up. As long as the whites of the eyes didn't get pink and irritated. The eyes were definitely more glossy than usual during the discharge time.
Good luck. I would save yourself a trip to the doc unless you see other concerns. My first daughter would get the discharge so bad that it would seal her eyes shut, so I would apply warm washclothes to wipe away the muck. Again the eyes were not pink, so I knew it just had to clear on its own with the cold.