Hey, congrats on your new baby and congrats on your decision to breastfeed. Maybe in Germany it's more common than here, but I'm always thrilled to see a bfing mom. I have breastfed 2 babies into toddlerhood, and it can be a confusing journey sometimes, but you can overcome your obstacles.
Try breast compression to get the milk flowing and keep your baby awake.
http://www.drjacknewman.com/help/Breast-compression.asp
This is a fabulous technique that works super well and will help fill her up before she konks out on you.
Also, it's important to ensure you have a good latch. Poor latch can mean baby isn't transferring enough milk and the supply/demand of breastfeeding is not properly triggered, affecting your supply.
Make sure she's not just sucking on the nipple, but has a nice big mouthful of areola. The asymmetrical latch is an excellent way to ensure you have a good latch (it's the only technique I use :) )
Here's a bunch of videos on proper latch:
http://www.drjacknewman.com/video-clips.asp
I wouldn't worry too much about her using you as a pacifier. In these early days, it's all about supply and demand, and the more you nurse, the better your supply will be. Later on she will not need to nurse so much. But if you can get her to drink well at feedings it will spare your nipples some discomfort, so it's worthwhile to try. Many babies want to nurse lots in the evening, and that ok.
If her weight gain is good, per your midwife appts, you do not need to worry about not making enough milk. If you see lots of pees and poos, it's another good sign.
It's true that babies who aren't getting enough can become bored and fall asleep at the breast, but if weight gain and output is good, you can toss that worry aside.
Another good breastfeeding website is www.kellymom.com.
If it turns out you are having trouble with your supply, check out:
http://breastfeeding.suite101.com/article.cfm/new_researc...
this article links to many other on reasons for low milk supply, using at-breast supplementers, etc.
In the meantime, though, work on that latch, use breat compressions, and enjoy your babymoon. the first 6 weeks are the hardest, but before you know it bfing will become second nature to you and your baby.
Good luck and feel free to send me a personal message if you need more help.