My girlfriend went off to Canada.

Literal

I [of-の] girlfriend [topic-は] Canada [to-へ] went-ended-up.

彼女 literally 'that woman' is the standard modern word for 'girlfriend' — also simply 'she' depending on context, with only the possessive-like 僕の彼女 clearly disambiguating. ~てしまう here marks the going as a completed, possibly regrettable or finality-laden event. Combined with the past いった ('went'), the result is 'she's gone to Canada' with an emotional weight of loss or distance.