This is great that you want to continue giving her your milk, nature's perfect food for her. Unfortunately, breast-pumps are poor milk-extractors compared to babies, and your milk supply is based on "supply and demand," so if you're not able to pump much, your body is going to decrease your supply. Perhaps you can rent or buy a better pump (perhaps used? look on craigslist, cheapcycle or freecycle), because cheaper pumps tend to have poorer milk extraction than more expensive pumps. Also, if your daughter isn't going to nurse at all, a double pump can reduce the time spent pumping because you can do both sides at once.
Part of milk let-down is emotional -- some women just have a harder time with let-down with a machine, compared to their beloved child, y'know?
Pump, pump, pump. In my experience (pumping milk for a friend's adopted baby), I was able to increase my supply by pumping a lot -- again, "supply and demand." It may have been relatively easy for me because my baby was a newborn at the time, and I was still in that hormonal postpartum phase where the post-pregnancy hormones help start milk production, but I think it would be at least somewhat applicable to you.
What I would do is I would pump milk until I got no more, and then sit and "dry pump" for another 15 minutes or so. [During that time, a single drop would fall every so often, so it wasn't totally "dry", but it certainly wasn't a nice, steady stream like at the beginning.] Over the course of 6 weeks, I went from collecting maybe a few ounces per pumping session to collecting 25 oz in just the morning pumping session (although I did usually sit for an hour that session). Since your situation is different, I would suggest pumping multiple times during the day, but preferably about the same time of day each day, and also that you sit and pump as long as you reasonably can, even though you won't get anything for much of that time. Within a week or two, (probably within a day or two, but give it more time, just in case it takes longer) your body should respond to the increased demand with more milk.