No, I believe baby's tears has smaller leaves. This looks more like a peperomia, perhaps Peperomia hoffmannii. I have included a photo of this peperomia, but it is mature with flower stalks. I have posted your photo with a plant ID group, and will let you know if the consensus is different. Peperomias generally do best if the soil is allowed to dry out between waterings.

It is now looking like your initial impression is correct. It appears to be a variety of baby's tears, Pilea glauca Red Stem Tears. Below is a link to more information. It doesn't specifically mention your plant, but I believe the care it describes is appropriate. I have included a vendor photo of your plant, but over time it will develop a more trailing habit. http://houseplants.about.com/od/foliageplants/p/Pilea.htm