Most relays have a "safe operating region" diagram. This will indicate boundaries as a function of both voltage and current. There will usually be separate plots for AC and DC as DC tends to arc whereas AC arcs will self-extinguish upon zero crossing.
Generally, there is a "maximum voltage" and a "maximum current" that are reached and some sort of derating (usually just given as linear) between extremes. The points where you get into the derating vs. voltage/current "hard limits" are device dependent. Without such a plot, assume that even at 12VDC, you can't go above 1A on the contacts.
If you have a real datasheet (not just a little glossy info sheet), it should have this plot in it as well as a ton of other data which may or may not be important to you.
Switching the primary (input) side is no problem here, though, as previously mentioned.