Advice for dealing with stepchildren?

I have been married for 3 years, my stepdaughter lives with us. We used to get along really well, but recently things have gotten really bad. I don't quite know what started it, but I have been really angry with her lately and she seems to do things to try to make me look bad all the time. She's 9 years old. For example, one night my husband went to the store, stepdaughter was in the shower, I went out on the back porch to water plants. About 5 minutes (literally 5!) my husband comes outside and says,"Do you want to know where Alice was?", I shrugged and replied,"In the shower?". No, she was across the street at the neighbors house, crying and saying that I left her home alone! She claims that within a 5 minute time period she completed her shower, got dressed, walked all around the house calling my named, walked outside and called my name, and determined that I wasn't there. ALL LIES! We have french doors leading to the back porch and I certainly would have heard her yelling through those! They're not soundproof! So anyway, since then I have been terrified that she is going to make more false allegations of abuse or neglect and so I have been very short with her and refuse to be around her alone for long periods of time. This may seem extreme, but I have seen many other step parents who have been charged with abuse because of lying stepchildren. And my husband takes her side all the time and makes excuses for her. I am 3 months pregnant now and am considering leaving if things dont improve. I can't live like this in my own home. Any advice or experience with this?