Single mother needs room with child

I'm a 45-year-old recently single mother. My 11-year-old son and I have been living in a coworker's guest room since my ex left us, but that coworker is moving, and I can't afford the rent on the house we shared on my own. I'm a working professional, and he's well-behaved and goes to school. We can't afford an entire apartment right now, as I'm saving up to buy a house for us.

I don't smoke, drink, or do drugs. We have friends we intend to spend time with on my days off -- so you'd mostly only see us in the mornings before work/school and in the evenings just before bed.

We do have a cat, but because our situation is temporary and our ultimate plan is to buy a house, we have a friend willing to watch her if we pair with someone who cannot have pets.

Willing to sign any lease up to and including a full year.

Since I will also have my child with me, I intend to run a background check on any co-occupants before signing or paying anything. I don't have an issue with past drug offenses (everyone makes mistakes and should have the opportunity to start over), but violent offenses would be a dealbreaker. (If you're an ex-con with another kind of offense, I'm happy to discuss your unique situation with compassion, as long as you're open with me.) I myself do not have a criminal record.