Nursery rhymes are a great place to start when learning any instrument. They're also great to use as a vehicle to learn by ear! Try using the hide notes, focus feature, and tempo control to learn this one. Make sure you have your A major scale down and take it a measure at a time. You can do it. The full version of this tune has alternate picking, but if that's too tough you can use the difficulty slider to simplify the tune even more. Simple versions of tunes without sixteenth notes are great for learning by ear and make it easier to play the tune at a faster tempo!
Check out those little dots above some of the tablature notes. Do you notice how they sound different than the other notes? Those notes are played short, or staccato. To achieve this effect with open strings, lightly lay your fingers flat across the strings right after playing. This will deaden the note, and cut it's sustain short. To play staccato with a fretted note, keep your finger in contact with the string but release enough pressure so it no longer touches the fret after you play it.