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I wrote a letter to the landlord telling them about my family. We had no issue so maybe try that and include a picture
As far as the daughter being autistic there won't be anything in the application about her condition so I wouldn't worry about that. It will ask you jf you have any dependents. If you and your partner both work and what income you have coming in. Alot of people board with friends or family so they will want a reference from youd nan. Good luck hope you find something nice.
You will need to show that you can afford the rent. Be prepared to show bank statements with regular income. Get your boss to be a reference. If you know a police officer do the same. A police check helps a lot as well
When we went from owning back to renting (we bought a lemon and had to sell the stupid house or go bankrupt) we ended up including references (phone numbers and details on how we know them ie bank manager, daycare provider) with every application and a brief written explanation of our situation. It worked for us.