Lets get some common terms out of the way.
Dining Credits - Disney Dining Plans include a certain number of credits, per person, per night of stay (hereafter pppn).
Snack Credits - Redeemable for small treats such as cupcakes, ice cream, popcorn and drinks
Quick Service Credits - Redeemable for an entree and dessert at fast food restaurants around the parks and at Disney Springs. (hereafter QS Credits)
Table Service Credits - Redeemable for and entree and dessert (and appetizer on Deluxe or higher plans) at Table Service restaurants (sit down restaurants) around the parks and Disney Springs. Table Service Credits may also be used at any Quick Service, if you so decide, but not vice versa (you can't use QS Credits at a TS restaurant). (hereafter TS Credits)
Refillable Mug - These are chipped mugs...no, not like Chip from Beaty and the Beast. Disney Resorts have a control system on their beverage bars called RapidFill that reads an RFID chip in your mug and allows you unlimited refills during your stay, but not before or after. The mugs activate as soon as you check into your hotel and pick them up from the food court, and deactivate at midnight of the last day of your stay. Mug washing stations (small sinks) are available at the bars as well, so they are easy to keep clean. The mugs only offer refills at resort food courts that have beverage bars. Not hotel restaurants, and not at the Parks or Disney Springs.
There are generally two flavours that people get with Dining Plans (there are more options, but these are the most common). Either:
Disney Dining Plan (DDP) - ($60.04 per adult per night, $19.23 per child over 3 per night)
1 QS Credit per Night of Stay per Person
1 TS Credit per Night of Stay per Person
1 Snack Credit per Night of Stay per Person
1 Length of Stay Refillable Mug per Person
Deluxe Dining Plan (DLX) - ($109.53 per adult per night, $29.86 per child over 3 per night)
3 QS/TS Credits per Night of Stay per Person
2 Snack Credits per Night of Stay per Person
1 Length of Stay Refillable Mug per Person
Your 3 month old is not eligible for the Dining Plan (for obvious reasons, though the cutoff is age 3 years). The rest of you will get credits per night of stay. So, for a 6 night stay, you'll get...
DDP ($835.86 or around that will be your cost)
6 QS Credits per Person (18 total)
6 TS Credits per Person (18 total)
6 Snack Credits per Person (18 total)
DLX ($1493.52 or around that will be your cost)
18 QS/TS Credits per Person (54 total)
12 Snack Credits per Person (36 total)
All of your credits will become available for use as soon as you check into your resort, and will stay active for use until midnight of the day you check out. Also, while Disney doesn't really advertise this, the credits may be used at anytime during your stay by anyone. So, even though there are Child Credits vs Adult Credits (in price), in practice, the system doesn't know. The credits are assigned to a lump account that is linked to your room, and as a result may be used by anyone staying in that room at any time.
Your child will be limited at most restaurants to the children's menu (as most restaurants have a children's menu). My kid is ok with the stuff on the kid's menus (except Meaty Macaroni, she's not really a fan of that), but there aren't a lot of choices. Chicken Nuggets and the like are on some menus, but not all. So, it's something to consider. All current children's menus are available online at Disneyworld.com
The current costs are really something for you to figure out. You can come out ahead, but not necessarily.
Try using this site to play around with your dining options and the costs to see if it's a good value for you or not.
http://www.distripplanner.com/
While the plans cover the cost of food and non-alcoholic beverages, they do not cover the cost of tips at Table Service restaurants, or alcoholic beverages.
Hope this helps!