Hello yes I did it in the past. Rented my place out as I was transfered interstate for work... so kind of same situation but different reasoning!
No the shortfall is not tax deductible on your rent, however the rent you received and your mortgage payments have tax implications - you are able to avoid capital gains tax for up to 5 years as the house you own is still your principle place of residence as long as you don't purchase another house. If you receive any family payments these may be effected as the rent you recieve for your house becomes income -regardless of the rent you personally pay out. If I was you I would defintely make an appointment with your accountant to work through the scenario