I nursed 2 babies so far - another on the way. Both of them nursed for very short periods of time. My "let down" is VERY fast. Actually both of mine would throw up - I mean major projectile type requiring both them, me and the chair to need a change - if I let them go much longer than 5 minutes...especially in the beginning. At the beginning they would only nurse on one side per feeding. I'd alternate sides for feedings instead of doing both each time since it was such a short time. I worried about the vomitting at first but then I pumped a few times and realized that I was overfilling 6+ ounce bottles in less than 5 minutes on the low pump setting per side. Many times I could just turn the pump off and I'd just continue to spray into the bottle it was so strong. I think they start bottle fed newborns on about 2 ounces/feeding so 6+ ounces was way too much! We realized that the babies were simply overeating because they wanted to suck still even though their bellies were plenty full. I reduced feeding times to only 3-5 minutes and they had full bellies, but didn't explode. Have you noticed that you tend to leak a lot or spray when you take a warm shower? You may have a quick "let down" as well. So, YES... it is definitely possible your little angel is getting enough milk in just a few minutes.
Just continue to monitor her diapers - it will be your biggest insight into how she's doing for the early months. As long as she's producing there, she's getting enough in. Mine would poop during just about every feeding -- at minimum. One of my friend's breastfed babies only pooped once a week - both are normal for breastfed babies. There should be lots of wet diapers for all babies though so if she's not making wet ones, talk to the doctor.
Usually the ped will want to see babies by 2 weeks...sometimes also at 1 week for breastfed babies. They basically just do a weight check at this point to make sure they are starting to regain weight at 1 week and are back to birth weight by 2 weeks. That's another way they can monitor if the babies getting enough milk.
Another thing to remember as a new mom - call the ped anytime you have a concern or question. Use reason, of course, and only call about serious things during off hours, but during regular business hours, don't hesitate. Many times they will have a nurse call you back to review the concern with you and advise you about making an apt or how to deal with it at home and what to watch for to know it's something needing checked in the office. Don't feel silly about any question or feel like you are bothering them. If you don't know, that is what they are there for. Most of the time a quick phone call can ease your mind and help you to know how to handle a minor situation without too much stress.
Enjoy your new little princess!