If you need to catch up on zzzzzzs I'd try adjusting your sleeping habits before you tackle hers. Just take the phone off the hook, and sleep until DD wakes up.
Stimulating her in the day so she doesn't want to sleep, try playing, take her for a walk outside, tempt her by nursing or if you are up to it, give her daytime bath. I know you're shattered Purplecatti otherwise I'd suggest carrying her around a lot during the day. On the other hand, overstimulation could also contribute - she might be shutting out a loud and boisterous daytime atmosphere by sleeping through it.
During the day, you can talk directly to DD and play with her. At night, stick with low light, lullaby singing and quiet cuddling rather than direct eye contact. She's not wakeful because of over-heating is she? an above-normal body temperature could lead to wakefulness.
If she wakes up DD may not require instant attention if she's in a secure and interesting place. Eg a low light on and a few soft toys with her, or stickers on the ceiling to make it interesting.
Are you drinking too much coffee, tea, coke, ie containing caffeinewhich passes into breast milk? I wonder if you could cut down on if not avoid caffeine for several days. A neighbour of mine who was bf had to avoid drinking coffee after 3 pm.
Is DD ever "colicky"? Again not blaming you but maybe she is sensitive to food you eat and pass through breast milk. Evening might be the most painful time and morning more comfortable for her. That could explain her tendency to prefer sleeping during the morning.