If you KNOW she isn't feeding effectively then sometimes it is necessary to pump to stop from getting mastitis and to have milk to supplement her with. However 4 days old is probably too early to tell how effective she is at feeding as your milk will only just have come in properly, she might well still be losing weight or not back up to birth weight (and that is normal).
How are her nappies? If she has passed her meconium and poos are getting lighter and yellower in colour then its a good sign that she is feeding well and you don't NEED to pump.
How are your nipples after feeds? If you have no damage and they come out without looking squashed or angled then again it is a good sign she is feeding effectively.
A bit of info about "full" breasts and "filling up": This isn't how human breasts work. We have no real space to hold milk in our breasts (hence why they leak when baby hasn't fed for a couple of hours). We over produce milk as a consequence of hormones produced after birth but once supply has settled down our breasts never really fill up, they produce milk as needed. When milk is removed from the breast prolactin levels increase telling the body to make more milk more quickly. when milk remains in the breast, prolactin levels fall and the body makes milk more slowly or stops. So empty breasts mean making more milk. Yes your baby will be frustrated that there isn't an easy supply of ready to flow milk after you have pumped but your body will be producing it constantly - she may just not want to work for it.
Simplest (although not always easy) thing at this stage is to try to get baby to feed as regularly as possible. Keep her near or on you so that she can get to your breasts whenever she wants to and if it is going beyond the 2 hr mark between the start of each feed then make an effort to wake her (strip her down etc.). You only need do this till she makes back her birth weight, then you can follow her lead more.
If you do want to pump sometimes and she wakes right after its not the end of the world. If she gets frustrated then you can feed her a little of the expressed milk to calm her (say 5 - 10ml) and then try her back on the breast. The more she sucks from a not-engorged breast, the more she'll stimulate your supply and the more fat content she'll receive in the milk itself. Little and often is usually the way babies want it!