Hi Kate
In that newborn stage babies basically just eat and sleep. You may get up to half an awake and happy after a feed, but mainly if baby isn't feeding then she should be sleeping or trying to get to sleep.
What are you doing to help her sleep?
My recommendations would be a bouncy chair (minus any play arch) for hands-off foot bouncing to sleep and a dummy, to allow for comfort sucking.
If you are doing all you can to get your baby to sleep and she still isn't, my next suggestion would be to consider if hunger is a factor - since a full tummy usually gets a newborn to the 'milk drunk' dozy, malleable, easy to sleep stage.
If you are already working hard to get constant sleep and you are confident she is feeding enough, then the next suggestion would be pain from wind.
To answer your questions - good sleep tends to promote better sleep and unfortunately poor sleep promotes worse sleep. So I would look at working very hard to get her to sleep more. Getting good sleep habits and lots of sleep are really important.
But shorter catnaps (of, say, 40 minutes) are common so don't be put off that you don't get naps of several hours in the daytime - that won't happen until somewhere around 4-6 months. Newborns need to feed more often than that through the daytime.