You certainly may rent another property for yourself as long as you can afford it.! If I may share some words of Wisdom. Have a cushion just in case the renter for your house experiences any hardship that might effect their payments to you, and try and make sure that your are not relying on their payment to cover the rent where you will be renting.You should be okay!! Wishing you the best with that!
You should be able to if your credit is good and you have proof of income. Just show the prospective landlord your rental income receipts (proving you are receiving money from a renter).