Are we changing nappies with every nighttime feed?

When LO wakes up, I take her out of the room to the feeding chair (keeps me awake! In bed I'm liable to doze) then burp her, then change her, then get her back to sleep having riled her up with the change (no point doing it first as she usually wets or dirties the nappy while feeding) then bring her back to bed. Usually takes 45min-1hr which isn't too bad, but it means that in 2hr gaps between feeds I'm only getting 1hr sleep (luckily LO usually starts the night with a long 4hr sleep, then the intervals get shorter). I hear about mums "rolling over to feed baby then going back to sleep" which implies no nappy change, but whenever I change a night nappy it's always either wet or dirty, never dry and clean, so I feel like I don't want her to lie in that... but also, I could really use the extra sleep! So what's everyone else doing?

EDIT: totally forgot to say baby is six weeks old!! She's gaining weight beautifully.