If you're interested in some practical advice (not related to R-Pi at all) as a parent of two young kids I ended up with two baby monitors. One is an audio/video monitor, and one is audio-only. The video one uses some undisclosed data protocol, likely similar to bluetooth (camera and monitor must be "paired" before operation). It has about 0.5 second delay from "real time" but that is not a big issue: the video is just there to determine if the kid is awake and upset or about to crawl out of the crib, or is just making noises when asleep. For this, even 4 seconds latency on video might be OK. But to be honest we normally just use the audio-only monitor, because the video one has a built-in non-adjustable mute level so only cries a certain level above background ambient ever get transmitted. By contrast the audio-only monitor can be turned up to monitor the ambient so even quiet noises can be heard. Then we can turn on the video as needed to confirm the situation, before actually getting out of bed to check in person.
In case of interest, the video system we have is the Safe Baby 2-Camera Monitor
(which is apparently no longer available, but no doubt similar systems are).
What might be really useful is (assuming you have a smartphone) sending the baby's room video to your phone, if you could do that in quasi-real time, thus avoiding the need for a separate display, and using something that's easy to carry in your pocket. Most baby video monitors are significantly thicker and more bulky than a smartphone.