My son (my first baby) was very difficult as a baby and I really did struggle. He was never happy, constantly grizzling, tired because he was up screaming all night and up early in the morning. I really couldn't take him anywhere, baby groups or visiting friends were a nightmare because he would just grump and scream.
He improved a lot when he started crawling, even more when he started to walk, and was so much better when he could play with toys properly - shape sorters, pushing cars about, putting things in and out of other things and so on. Now he's nearly three and he really has been a lovely toddler (so far!). It was almost as though he just didn't like being a baby. Of course he has his moments, but it is really wonderful how much he has changed, and I can promise you that it will get better (well I can't promise that the sleeping will unfortunately, we suffered for some time with that, but it's better now).
My second baby is 6 months now and I can see just how grumpy he was. Of course like all babies she needs constant attention, and her sleeping is also pretty rubbish, but she just seems a happier baby somehow.
It will get better, they change so quickly. The sleep deprivation makes everything so much harder, especially if you talk to friends with babies that sleep long stretches every night. In a few months time your daughter will be crawling about, then walking, then playing properly, and things will get a lot more fun. It is the way that she is at the moment, but she won't be like that forever, if that makes sense!