My son is a year old and he just broke out in a body rash that appears to look like hives - he is cutting back teeth - could this be the cause?

No : No teething is definitely not the cause of an all over hive-like rash in a 12 month old.

Unlikely: These events are not related. More likely, your son has caught a viral infection which may lead to skin rash or hives. If this is the case, the problem may become more severe for a few days before it starts to fade away over a period of days or weeks. If it itches try antihistamine. (this is assuming that a drug reaction is not the issue)