If you're playing along with the Carthy CD I make it c# and g#7 and maybe another I cant quite fathom.
But guitarists can probably use those g-clamp things and just play chord I and V7.
The insertion of a bar of 3/4 in a jig (or conversely 6/4 in a 3/2 hornpipe) is common in both folk and classical music, and here the first two beats (ie 2 dotted minims or crotchets) become a triplet (ie 3 minims or 3 crotchets, depending whether you take it as 9/4 or 9/8), the 3rd beat remaining as 3 crotchets or quavers.
Even with some words the tune sounds perfectly sensible in straight 9/8;- Jen-ny come| Back toyourlittle| Ba-a-by
It sounds like a pipe tune, so in the original it would be very difficult to tell where the beats were anyway.