I know this is about a year late, but....
My daughter and I have been playing this one quite a bit lately, and struggled at first with the key, but I think we have it figured out now. Trying to determine the key by looking at the chords and finding two majors a full step apart won't work here. The chords used in order of appearance are:
D D# E F#m G G# A Bm and C
This is kind of a mess. We can eliminate C because the Bm and the F#m don't fit, they should be Bdim and F if it were. The D# is only used as a "passing chord", I'm not sure if that is a real term or not, but it is just a stop on our way from D to E and pretty obviously not meant to indicate key in any way. If we drop out the C and the D# chords as just outside/passing chords, we can make a good case for either D or A so I sat down to work it out by ear on my guitar and got through the whole melody in A starting on E to be A mixolydian, which makes a lot of sense and fits in with the common structures of Hunter/Garcia songs.
However, my daughter was having trouble singing it that low, so I re-keyed it to D starting on A to make it D mixolydian (because that also fit well with the rhythm chords) and we were goofing around with that for a while and it sounded good. Then, last month I got DP 20 which has this song on disc 1 and I started playing along with the boys, and lo and behold, they play the thing in D, so I think that is the real answer, it is D mixolydian.
However, just because I had put in the work on the key of A, I started singing the Key of A version during the "Did you say your name was...." and "I'm gonna sing you...." parts as a back-up line to my daughter's lead in D, and although we think it needs a lot of work, we think it sounds pretty cool. The only difference between the two keys is the sharp 7th in A (Gs are sharp) that is natural in D. In those chorus parts, there are no 7ths so the key of A version matches up perfectly with nothing outside the key of D. Singing the verses in A works because the only time the 7s appear, the rhythm chord is an A, so no worries of sounding like a clam there, we just didn't want to overuse the harmony.
I tabbed the melody, Key of D version, in a word file if anyone is interested in it. I could also do the Key of A version with minimal effort if someone wanted that too.
Mama Mama many worlds I've come since I first left home.