Starting to pump milk this late in the game?

Hello everyone. I have a 10 month old daughter who has been exclusively fed. She is getting close to the one year mark, and we are starting to think about weaning. She has never taken a bottle well, and she hates the taste of formula. I recently bought a pump, os she can have the flavor she loves in a cup. I would love to start replacing a few feedings a day with this. I am lucky enough to stay home with her. I am just so unsure when to pump! She is still establishing a schedule, and I nurse on demand. I would say she goes about 3-4 hours during the day without nursing, and 7-9 hours over night. I know that milk is produced on a supply and demand basis, and that the is never "empty"... but, the two times I have tried to pump so far I have gotten pretty much nothing. On one side less than .5 of an ounce. On the other side the amount was so small it was unmeasurable. Help!