When looking after my niece I have a Sonic Alert Sonic Boom Alarm clock (with receiver), and a baby cry monitor. I also have a baby monitor that senses that the baby is breathing and will alarm if the baby stops breathing.
I put the babycry monitor in her room, right by her crib and where the baby monitor alarm is ... then if she cries or is in trouble (breathing problem) the baby cry monitor will "hear" either her crying or the alarm sounding. The baby cry monitor then sends a signal to the Sonic Boom alarm clock for me and it either shales me, or flashes a light (my choice).
I'd recommend that you get in touch with a local Deaf Resource centre, or Vocational Rehab place that specializes in Assistive devices for Hoh/Deaf as well as helping parents-to-be (or new parents) learn what is available to facilitate taking care of their infants etc.
For what it's worth - I personally would NOT recommend relying on a Hearing dog (especially one that isn't professionally trained and certified as a hearing dog) for knowing when your infant is crying etc in the night ... for a number of reasons. They may be an additional "back up" - but I'd personally what something like a monitor/alarm etc combo.
Also - if you do apply for a Hearing Dog, make sure that from the very first application etc you stress that you will be having children, and that your hope is that one of the dog's main responsibilities will be listening for the infant/ child. This will impact what kind of dog they train... and they will be able to tell you if a hearing dog can be trained to do this reliably/safely or if that is something that isn't realistic to expect from the dog.
Hope that helps!!