Let's get straight to the point, the most important prop to bring to a family photo session is.... your kiddo's favorite lovey, toy, blanket, etc. Whatever that thing is that your kiddo can't put down or sleep without, bring it!
The photos with their toy may not be your favorite, it may not be the one you hang on the wall or put in a photo album, but it will be one you cherish for a lifetime. It will be a memory worth treasuring when in twenty years you can't find that lovey anymore and your little one may have forgotten all about it. If your daughter loves her princess heels or your little guy loves his newest car toys he just got for his birthday, it's all a memory worth saving.
Doing an at-home lifestyle session makes it easy to catch these memories because you are all in your own space, with all of your own favorite things, capturing life in the most authentic way.
If you're not doing an at-home lifestyle session and you're meeting for an outdoor family session, then you may want to hide the item in a backpack or purse for a while if you want to try and get some photos without the item, but if your babe is struggling with feeling comfortable in front of the camera OR you simply want to catch their real personality, bring it!
Also, don't forget your older babies too... they still play with toys and you may want to hide it in your bag as well.. LOL!