What would you do?

Hi, I'm needing answers on this particular question. Okay, I have a 5 month old baby. I'm a teen mom. My baby's father is currently incarcerated but we are still together. (Please don't say anything about him being incarcerated) We visit him once a month, on Saturdays, because that's the only day that's most available and convenient for us. I do this so my daughter can have an idea who her father is(since she is SO young) and for my baby's father to be able to hold and talk to our daughter because he isn't around 99% of the time.

I'm planning on working, I am available every single day out of the week except the Saturdays when we go see him, once a month. I honestly don't know what to do, should I apply and say I'm not available on Saturdays, or should I tell them the situation? My counselor told me not to tell the people who interview me that I have a baby because it is like a "red" flag to them. "Red flag" as in they think of emergency, days I have to take off because baby is sick, etc. She told me to just tell them when they ask and that I have a great support system as well. Should I disregard her advice and just say I have a baby upfront? I just honestly feel like nobody would take me because I'm a young mother with "grown-up" responsibilities. :( All Im trying to do is financially support my baby. I get tons of support from her father side and my side but I just want to be able to do all of that. I just feel hopeless.