Your daughter is only one month old - think of it this way, she spent 9 months being in a dark, warm womb close to you and then suddenly she's brought into a HUGE, bright world with loud sounds and noises. It's real easy to overstimulate a newborn, and thus they get tired easily too!
It takes time to build a routine and takes time for her to adjust to things too - get her to understand the concept of day and night first, dim the lights and reduce the stimulations (eg. lights, sounds, activities) so that'll help letting her know that night time is for sleep.
In the day time, she's likely to want to stick to you for the whole day - being in your arms or at least close to you - you're the only familiar person she is closest to! You can spend time just lying down and playing with her in the day, then do "cool down routines" to ease her into the sleeping mode - they don't need stimulants like music, sounds, lights, toys or anything like that until 4-6 months old so you can just spend time snuggling with her! To help you get the rest you need, breastfeed in a comfortable position and sleep when LO sleeps :)
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