This article from the Associated Press implies that the bill is still unlikely to pass ... but it has passed one hurdle.
Personally, I would not be buried with my pet, but it would also not bother me to be buried nearby someone who was with their pet.
However, as this article points out, many cemetery owners are opposed to the bill because they must account for all religions, faiths, and beliefs. And some religions, like the Muslim faith, for example, would consider it an insult to be buried near an animal. This is a very good point.
And with funeral homes, I don't think regulations are quite so simple that a funeral home could chose not to offer a legal option. So, it may not be as easy as saying that some cemeteries can have pets and some can't.