Oh my goodness yes, it's normal and expected and an entirely positive sign. The worrisome thing, in newborns, is when they're very groggy, and it's hard to get them interested in nursing. Frequent nursing is exhausting for you, but it just exactly the right thing for baby. That frequent demand is going to stimulate your breasts to bring your mature milk fully in, which takes a week or two. It's also going to set the stage for a good full reliable supply in the long term-- up until a few months old, the supply is largely regulated by keeping your hormone levels high-- you need to nurse very frequently to have that happen optimally, especially at night.
Remember that nursing is more than just food, for an infant. It's comfort and security in a brand-new, often scary world. It's a re-connection with you when baby feels lonely or overwhelmed. It's a way for baby to reduce stimulation and wind down to sleep. It's incredibly rewarding for baby, because of the wonderful hormonal interactions that happen between you and baby when baby suckles. And it also helps your body to return to a normal, non-pregnant state.
If you're finding it wearing, it can help a lot to learn the side-lying position, so you can nap while she's nursing. Choose a flat, firm mattress for this, not a sofa. You do it by lying on your side, with one arm up under your head and one embracing baby. Put a rolled up towel behind her, (tape it so it stays rolled) to support her lying on her side. It can help to swaddle her, if her hands get in the way. Then you lie her at breast level and help her latch on. I found in the early days I had to latch mine on while still sitting up, and then ease down to a lying-down position.
Make sure there's no loose bedding near her that could get over her head, and then relax.
I can't imagine surviving the early weeks without being able to sleep through feeds. I would have gone completely nuts.
Learning to nurse while carrying baby in a carrier or sling is another skill you can start to work on, when you feel your energy coming back, and want to be up and doing things during the day. Baby can nurse until she's sleepy, and fall asleep right in the carrier, keeping your hands free and getting you up and about.