Could be teething, or an ear infection or she might be starting a cold. Its hard to know for sure but you should call the Dr. She's definitely not feeling well and when they're that little its better to be safe than sorry
Take her temp too and try just giving her a couple ounces of water. You don't want her to get dehydrated but sleeping/sluggishness is a sign she could be getting sick
How long has this been going on?
My son was like that, nine months old now, turns out he was having a growth spurt, but I would give your doctor a ring just in case, just keep trying to feed her, if your breastfeeding then keep her against your bare breast if bottle feeding take a syringe and feed her. Even though I'm breastfeeding my son sometimes just want to latch, around the time he started teething, had to express and feed him from a syringe
At one point I was doing both bottle and breast because he was a hungry baby and breast wasn't enough, he would pick and choose if he wanted breast or bottle. Lol it was so annoying! :)