Well done on the 6K Peggy and welcome! If you check out the pinned posts here you'll see that ju-ju- has created a weekly training plan for runners wanting to get to 10K.
Another option is to do your own thing by running 3 times a week, 1X 5K, 1X fast or interval run say 3K and then your longer run where you increase your distance gradually. Please do not increase your mileage every run as you mentioned in your post. This way injury lies ☹️ Just follow the Golden Rule of not increasing your total weekly mileage by more than 10%.
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