You start weaning when you offer something else than a breastmilk (or formula). Mainstream pediatricians recommend to start offering solids after 6 months. As previous poster said, it is up to you and your baby to decide what is a comfortable pace for introducing solids. Some babies don't really want or are not developmentally ready to start solids at exactly 6 months. 6 monhts is a general outline and your baby may be ready a little bit later or much later.
Simply, some babies are great solid food eaters from the start and some are not. I advise to follow your baby and see how much he or she can eat. It is ok to back off if you see this isn't working and try in a couple of weeks later. I tried my dd on solids when she was 6.5 months and she didn't really want it. We waited two more weeks, she then had very little and she continued on very little for a long time. I think my breastmilk was 90 percent of her diet until she was 11 months. Then, all of a sudden, at one year she started eating LARGE LARGE quantities of food, and she was eating everything there was on the table.
So, my opinion is that there is no such thing as a window of opportunity to introduce solids, I know quite a few babies who were solely on breastmilk till one and they are healthy, eat well solids now.
I am actually quite surprised about your pediatrician, it is uncommon approach. This type of breastfeeding is called ecological breastfeeding. But to make this working you would have to nurse more or less on demand, you can't schedule your baby's feeds and then rely on 4 or 5 nursings per day only. This can only work if you nurse a lot. If this doesn't work for you, you will need to add some solids to your child's diet because she/he will need more to grow.