If you want to go to WDW to see it decorated for Christmas, my advice is to go during the beginning of the month. The decorations are up and the crowds will be much lower. The week between Christmas and New Year's is one of the busiest times of the year. I wouldn't go during that week, and would never recommend someone go during that time of year for their first trip.
Since you're on a budget, I would go during one of the times of the year when WDW offers either
free dining or kids stay & play free (free ticket for your child). Both of these can big huge money savers.
Like others have pointed out, the only way you can save money is either by increasing your income, or cutting your expenses. While we don't live paycheck to paycheck, I cut corners in a lot of other areas so we can fund as much travel per year as possible. Some of the things we do are:
Don't eat out at work (other than once in a while. I've been in my current job for over a year and can count the number of times on one hand that I've not brought my lunch to work).
Same with coffee, bring your own to work (unless they offer free coffee where you work). I used to stop at Dunkin Donuts every day. $2/day for coffee, 5 days a week is over $500 a year.
Reduce eating out. We used to eat out a lot. Now its about once a week and most of the time its take-out (chinese, subs, pizza). It save drinks and tips.
Use up leftovers. I plan out my meals for the week and plan to use up leftovers. This has helped me shave money of my grocery budget. I also meal plan before I shop which has helped to. One night a week we do breaksfast for dinner and another night we do soup (homemade) and sandwiches, again another budget cutter.
Have a yard sale, sell on craigslist or ebay to get rid of things you aren't using.