If your child isn't in day care and thus isn't playing with and in contact with children for much of the day, or if she doesn't have siblings, she may benefit from short play dates with other children. (Of course, even if she is in these situations, you can feel free to arrange play dates for her.) While children at this age mostly take part in parallel play — that is, not interacting as much as doing similar activities while next to each other — they still enjoy being near each other and watching each other.
If you can, be sure there are at least two of each toy the children will get to play with when they are together. One-year-olds cannot share. If they see another child playing with a toy, that is the one they will want. If a dispute arises over a toy, it is often easiest to distract them with another attractive item. Rather than point it out to them, simply start playing with something else. Your attention to another toy will be intriguing to them.
The most important thing to remember about play dates for one-year-olds is that one-year-olds are easily distracted and don't have a lot of patience for extensive interaction with each other. They only need an hour or two (at the most) of time together before they begin to want attention for themselves.
Also, if possible, at this age, you are probably better off keeping both moms or dads around for the visit, unless the child knows and feels comfortable with the parent of the other child. Finally, remember that one-year-olds cannot entertain each other. They will need you to be part of their time together and will look to you for ideas and interaction.