Your plan (save $600 a month) is not on track with your goal (retire in 16 years) or your current assets ($3000 in savings and retirement). You seem to want three things:
Spend money on compforts
Have a SAHP
Retire in 16 years
You get to keep two and right now you are choosing the first two. I would talk about priorities with your wife, if you decide that you want to save, I would fully fund two Roth IRAs, one for each of you, that gives both of you well protected assets, and it gives her something that is tangably hers in exchange for spending cuts that will mostly affect her.
The following are luxuries and should be on the cutting block:
$100 Fancy food - you mention organic, not name brand, cooking from scratch and Cheerios. Cheerios are the opposite of the other things you list, I would look into your values here.
$180 Gas
$40 Internet - you have data plans for emergencies and the library for everything else
$20 Hair
$60 spending money - your whole budget is spending money
$55 Household Goods - this seems high, split out disposable (tp, cleaner, printer paper) and new gadgets
$20 MediaOpEx
$10 Entertaining - why does it cost $ when people come over
$50 Dates - it doesn't sound like babysitting is in this, try free dates and cooking dinner for your wife
$50 Gifts - I bet people would love your wife's homemade soup
$50 Vacation
$5 (month) Zoo membership - does your 1 year old get more out of the zoo than the park?
$30 Chiropractor
$10 Gym - now you have a bike
You don't have to cut all of it. I would read this article for a realistic idea of retirement dates
http://www.mrmoneymustache.com/2012/01/13/the-shockingly-simple-math-behind-early-retirement/I would also advise having at least one months expenses accessable, right now you are looking to drain every account you own if you are out of work for a month. Best of luck!