Covering an infant's car seat or bouncy seat with a nice, thick throw (fur, chenille, etc.) makes a safe baby-poser. You can also drape the mother or father's folded arms and chest with a throw, and have them hold the baby in a way that the infant can be seen. Since you don't have a lot of experience or reps, those two methods would probably feel comfortable for you,and can be done without a lot of risk or hassle. When the baby is in a three-person, family shot, the biggest issue is to get the infant elevated, so the baby can literally be seen, head to toe, in the shot. The baby must be "shown"...you cannot have a half-baby-body type shot, or just the head and neck of an infant that age--the baby needs to be "up and in the shot".
As far as what TIrediron mentioned, yes, one single flash is ample. have the light coming in at about 30 degrees from one side. If you do not have an umbrella or softbox, you can actually bounce the flash off of a wall, or a wall/ceiling juncture, or off of a corner of a room, and in that way create a large source of reasonably soft light, with the people placed about 8 feet away from the light, so you get soft, fairly even light, without too much fall-off in intensity. You do however want a little bit of shadowing, to create some dimensionality. There's not really an absolute need to have that flash be off-camera; in fact, in can easily be mounted right in the hotshoe, and swiveled off to one side, and angled upward, so that you get a good bounce off of the wall or wall/ceiling juncture. Quite often at the wall/ceiling juncture, you want to have the flash head zoomed to 75 or 105mm, for a good bounce that delivers a decent flash power level on the bounce; DO NOT, in most situations, have the flash set to a wide-angle setting...the results are typically less than stellar in a living room type scenario.
Do not be surprised if you end up in a situation where the flash is pointed sideways at the 11 o'clock angle or the 1 o'clock angle, and also angled upwardly, or even angled up and backwards-facing, while aimed at a wall or ceiling/wall juncture. Give this a try before the event. Spend an hour trying this at home before the evewnt. And PLEASE, think very strongly about using ISO 320 or 400 for this!