There are three basic types of jig, the single jig, the double jig and the slip jig. Single jigs are usually in 6/8 time but sometimes in 12/8 time, double jigs are 6/8 and slip jigs are in 9/8 time.

A Fig For a Kiss

A popular tune using the Dorian scale is "A Fig For a Kiss". This is a slip jig and is in 9/8 time, that's three beats in a bar with the individual beats grouped in threes.

I have given a count of nine for individual notes followed by a count of three for the groups of notes. On the slow clip. The breathing places are easy enough to hear they could of course fall at different places, that is the choice of the individual.

On the faster clip there are a few tongued/slurred triplets here and there and I hang on to the top G on the first bar of the second part last time round. This just adds a little variety to the tune.

D whistle A Fig For a Kiss slowfaster

Donnibrook Fair

A popular jig in G with some short and long rolls. If learning the notes from the written music, get the tune and leave the written notes behind as soon as possible or even better learn it by listening and also listen to others play it and anything that strikes your fancy can be incorporated, the tune then becomes more personal to the player. If you just stick to the written notes the tune may become just a series of dots with no individual personality.

D whistle

Donnibrook Fair

 The Handsome Young Maiden

This jig in the key of A is good for practicing the G sharp. The fingering for G# can be found on the scales page.
Here it is played slowly and then a little faster. The tuning for the G# can be a bit off as in my clip, some whistles can sound a bit sharp depending on the fingering used. The most in-tune would probably be half-holed. 
The commas are possible breathing spots the note underneath (if there is one) can be dropped. The dash above and between the notes of the second bar, second section are cuts

John McHughs Jig

An easy jig which falls nicely for the whistle, in bar five the two D notes could be joined just to give a slight syncopated feel, this could be done on the second part with the consecutive G's as well. It's only a thought, just to give some slight change to the tune.
To give a real sense of this tune I have taken a recording by a Concertina player, I would recommend to learn the tune from this recording and throw away the dots... anyway here it is played on the concertina with fiddle and bouzouki. The player I believe is Christy Mac.