I think the best course of action is to contact some schools in Peru (maybe with the help of your girlfriend). They should be able to tell you which qualifications are recognised in that country. Ask them about job opportunities for people who have 1) no TEFL qualifications, 2) an on-line qualification and 3) a certificate that was obtained through face-to-face tuition. If you don’t get any joy from the schools, you could try the British Council. IATEFL (International Association for TEFL) might also be able to help; there is an international IATEFL organisation and national ones in many countries.
It might be possible to teach without a qualification in Peru; although this would leave you very limited as to job options. On-line courses have the benefits of being cheaper and more flexible time-wise. The down side is that you might not get observed teaching practice; this is an important part of learning to teach because you an experienced trainer watches you and gives detailed comments on your teaching skills. Check whether the on-line courses have options for observed teaching practice. Face-to-face training is most widely recognised and will open up the most teaching opportunities.
You could also look at my answers to similar questions in this forum.