missed this one yesterday.....
I love this tune and you've got the melody notes down. I'll throw another word at you - phasing (without the 'r'). Has to do with playing on the beat, maintaining a steady tempo. You speed up and slow down a little.... You might think about trying to use a metronome to keep it even. Slow it down as much as you have to to get it just right, and then gradually start increasing the tempo till you get it up to the speed you want. Don't cheat - if you can't play it slow, you can't play it fast either. Now if only I could follow my own advice, - I'm an excellent 'armchair' uker....
You might also think about doing something like ukeleletim (great job, btw tim!) - just record yourself strumming the chords nice and slow, make sure you've got the song structure down. Then you can use that recording as a homemade playalong track. I love to do this - it's fun, useful, and you get to hear what you sound like. Makes it easier to be sure a more complex melody is falling on the beat properly.
Just my .02..... don't want to sound like a know-it-all, but I struggle with these same things every time I pick up an instrument and this is what helps me the most.