Unique Renter. Would you Rent to Her?

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I always turn to this forum for advice, so here we go once more. With a two-level 1115 sqft very upgraded rental there has not been much success in finding quality candidates, of course the property is going on only a month on the market. However, one candidate, a newly college grad with credit scores above 750 applied. She's engaged and her fiance lives in another state and will be joining her. He will be unemployed while he looks for a job. She, herself is also unemployed but stated she receives oil royalties. The application listed her income as $3000 a month. The property is listed at $1600 a month. She brings with her a cat, dog and a bird. I'd love to get peoples input on whether they would take a chance on her or bypass and continue looking.