。
I'll keep you company for just ten minutes.
Literal
10 minutes [only-だけ] keep-company [volitional-おう].
だけ marks restriction ('only') in a non-negative way — distinct from しか~ない, which requires negation. 付き合おう is the volitional of 付き合う, here meaning 'I'll join you / I'll come along' — the social-companionship sense of the verb. Together, a friendly time-bounded commitment.