I agree, big mistake. A guitar is not a piano. Most people who attempt to learn piano fail, most who attempt guitar succeed, not because it's easier but because the approach is different.
If you try to learn guitar like piano you'll likely do the impossible, actually fail to learn guitar.
Here's how to do it. Pick a song you have on CD, something easy to sing with no more than 3 chords, preferably just 2. They'll be I and V7, or I and IV, or if you're really ambitious I, IV, and V7.
Now, very important. Don't learn it in 12 keys. Learn it in ONE key.
Much more important, don't practise slowly. Practise in real time, at tempo, along with the recording. The first few times you won't make all the chord changes. Be sure you get every I chord on time, later every IV, soon every V7.
It should take you no more than a week to be able to play along with a slow folk song, getting all the chords right.