Well, it turns out that there are mandolin-banjos with only four strings, so it's not out of line to tune a uke the same way. The difference in scale length is small (14" for a mandolin, and what, 13" for the uke?), but the strings from a uke set won't sound very good in mando tuning (the lowest string on a mando is the largest, while on a uke it's the next-smallest).

So if you're uke-oriented, use real uke strings and tune to C (gCea) or D (aDf#b). If you're mandolin-oriented, change that fourth string to a classical guitar 3d or 4th string and tune GDae.

Don't change to real mando strings, though, unless you're sure it's a mando-banjo you're dealing with. The heavier steel strings will do a hurt to the instrument, everything from pulling too hard on the neck to cracking the tuners (uke tuners typically have plastic parts which get a lot of tension from steel strings). If you have a good, beefy neck and a larger shell (like 8" or larger), you may have a mando-banjo, despite having only four strings. But those small-shelled (4-5") instruments with thin necks are ukes, and can't take the heavier steel strings.

And as for tuning to "My Dog Has Fleas," how can anyone remember that? What's the reference? If you memorize it, sure, you can sort of remember it, but it's better to have a whole song.

I offer here my uncle Buddy's Ukulele Tuning Song:
[Pluck one string for each syllable in the verses, and strum for the bridge. Use 0210 as the V chord in the verses, but the real I/IV/V chords in the strumming parts.]

  Wish I could play the ukulele, 
  I'd pick it up and strum it gaily, 
     V
  If I could play the ukulele 
             I
  Like this. /strum-strum-a-strum-a/
  
  Wish I could play the ukulele, 
  I'd pick it up and practice daily, 
       V
  Till I can play the ukulele
             I
  Like this. /strum-strum-a-strum-a/
  
  Bridge
  
      IV
  But then a certain Mr. G
         I
  Said, "It's an 'oo-koo-lay-lee'" 
          II
  So the reason I can't play it might
      V
  Be 'cause I don't pronounce it right, 
  
  So, wish I could play the oo-koo-lay-lee, 
  I'll pick it up and strum it daily, 
       V
  When I can play the oo-koo-lay-lee
  Like this: 
  
  /strum-strum-a-strum-a strum-a strum-a/
  
  
  Copyright 2001, James McNeeley
  

This won't really work, of course, since the alignment depends on the font, but it's a try.