Giving Baby's Breastmilk to Toddler

I was unable to breastfeed my almost 2 year old due to pre-term delivery. Couldn't even pump because I was on mag sulfate for a week before delivery, and my supply was non-existent. Baby 2 was born full term, healthy, and I am pumping at night to stock up for when I return to work. My oldest has had some stomach issues and I'm just wondering if it would be of any benefit to give her some of my extra breastmilk, or if it's a waste because her system is developed? Has anyone done this? To be clear I won't be breastfeeding my toddler, just giving her some milk in a cup. Thoughts? Advice?