Well something don't seem right with that. Kids her age should eb doing all of that.
Does she have access to an area to crawl and do things herself or is she in a crib,stroller,or play place a lot , can you describe the area she plays in ? Ask Mom to have her checked on to see if all is well,some children are late starters.,it may be as simple as that ,does your sister get plenty of interaction .games ,as her caring sister maybe you could help her .Good luck you are a good caring sister .
At the very minimum your sister should be sitting up. It's good that you recognize this is not normal. Does your mother not question this? She needs to get your sister to the pediatrician. You are a good, caring sister and she's lucky to have you!