It's an expression of surprise but is not widely used today. I wouldn't consider it offensive.
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The characters in Walt Kelly's newspaper comic strip "Pogo" used the exclamation "Dog my cats!" often as a funny cry of surprise, similar to "I'll be a monkey's uncle!" or "I'll be blowed!" It's not in any way offensive. Unless some cat took umbrage. And if she did, she's have to give it back, umbrage is expensive.