The copper wire resistance for 130' would be about .42 ohm (1.62 ohm per 1000') for 12 gauge. With a 10 amp load that would be about a 4.2 volt drop. For 10 gauge this drops to 1.02 ohm per 1000'. The 12 gauge run should normally not be a problem. As for the run itself, when you bury it consider burying a PVC pipe for a conduit and making it big enough to handle anything else you may want to fish at a later time. A lesson I've learned over the years is if you dig a trench to bury something once, chances are you'll dig again later for something else. Do it once. Pipe is cheap and it would give your dog another obstacle.
Al