Accidental landlord cautious about prospective tenant

I recently moved home and am looking to rent out my previous property. Given that I have moved over 200 miles away it was not a viable option for me to manage the property myself, so I joined a highly-recommended online letting agency. After a short while, a couple (both in their late 20’s) expressed an interest in renting my property.

As a first time landlord, I obviously wish to let the property to a sensible, trustworthy set of tenants who will ideally stay there long-term.

A number of issues have been brought to my attention which make me nervous letting to this couple. I wish to seek some advice on whether I should rightly be concerned or if I am being unreasonably cautious.

The female is currently pregnant and on maternity leave. As a result, only the male has been referenced by the agency and it appears that not only is his salary to rent ratio insufficient, he is currently employed on a 12 month contract as a teacher. They are willing to have the father (a doctor) as a guarantor, and state they can pay the initial deposit and one month’s rent in advance. I am concerned with their long term ability to pay rent (despite having a guarantor. I will also have rent guarantee in place throughout the duration of the AST). I maybe should also note that I have already conceded on allowing them to have pets in the property too.

Should I rightly worry about letting my property to these prospective tenants?

I am thinking the best thing I can do is speak to the tenants by telephone and ask them a number of questions to get a better feel for who they are and what their background is.

Any thoughts, comments or advice would be greatly appreciated.

Thanks

Ray