At age 7 your tama go would not really have a baby by now. My tama go is 8 and still there is no baby. I recommend you to wait until an egg appears on your screen (it means you have a baby coming!) It might take awhile for it to hatch but after the egg hatches your baby will stay around his/her parents for about 3 days.
My Tama is ten years old. Kuromametchi married the match maker. They are 10 years old and no baby. Why no baby? Friendship points are full, training is almost full, hunger always full, happy always full. Great care, but still no baby. Is there a way?