Hi Melissa!
Yes - in my opinion, Advanced Dining Reservations (ADRs) are a must for any vacation at Disney - especially during peak times. However, I don't think you have wrecked your vacation! Many guests don't realize the importance of ADRs until they actually get to Disney to begin their vacation! What you have going for you is time - approximately one month.
If you haven't already, I would recommend you research various restaurants on the
Disney dining page located on disneyworld.com. You'll be able to narrow your search by using the filters on the left. Because some of the more popular restaurants and times tend to fill up quickly, you may have slim pickings so do have back-up restaurants in mind when you call Disney Dining (407-WDW-DINNE). And there is always the hope of cancellations, so do consider calling back often if there is a particular restaurant you'd like to dine at.
And if all else fails, you may want to try a walk-up reservation. There is a possibility of last minute cancellations or a no show but to avoid disappointment, do have a back-up plan ready. I've actually had luck with walk-ups at 'Ohana and Whispering Canyon for dinner in the past. I have, however, been turned away at Crystal Palace and Chef Mickey's. If you decide to try a walk up for dinner, I would suggest you arrive early in the evening before it gets too crowded.
Sending lots of pixie dust your way to make this all work out! Diane :)