Totally normal for a 3 wo, in fact sounds like she's doing really well! She needs to feed lots to establish supply and to grow. Make sure she doesn't take any big breaks between feeds during the day so she's getting as many calories as possible in daytime, and that'll help her stretch a bit at night too, but her tummy is still tiny so be patient!
I did find that a DF encouraged a longer stretch as LOs got a bit bigger (anywhere from 6-10 wks). I did DF around 10pm, and while as a newborn they would both wake around 12, 3, 6, roughly, gradually with the DF that changed to 10, 1, 5, and then 1 am slot disappeared (yay!). So it was really worth it for me.
Try to make night feedings as relaxing as possible *for yourself*. I made the mistake with LO1 of getting my book out, turning the radio on, and I missed out on lots of rest. With LO2 I kept the lights low, did lots of laid-back BFing (also known as biological nuturing) and was much better rested. Have a look here:
http://www.biologicalnurturing.com/video/bn3clip.htmlA lot of people talk about feeding lying down, but that never worked for me. What did work was building a big supporting 'armchair' of pillows as shown above and relaxing into that. HTH!