Putting the Pearlburst effect onto your animal companions' claws or bite attacks is going to be difficult... mainly because, normally, you can't put enchantments on natural weapons. We'd probably have to homebrew a set of doggie dentures or something... then make a masterwork set, enchant them, break every one of Lucky's teeth out, and then have him wear dentures all the time. Did I mention those purple people people aren't exactly animal rights activists? Those panthers' claws were manufactured, and weren't put in nicely.
Putting the Pearlburst effect onto a person's weapon is a good bit easier. You can reverse engineer the Pearlburst spell the same way that most wizards invent new spells; it takes one week per spell level, and costs 1,000 gp for research costs (asking for consultants, testing spell components, etc.) per spell level. Pearlburst is a level 2 sorc/wiz spell, by the way... and since you have an example of the spell to reverse engineer, I'll reduce the costs (both time and, consequently, money) by one quarter. Then you can have someone with Craft Magical Arms and Armour put it into a weapon like normal. (if you ask a wizard to enchant it for you, though, you'd need to reimburse him the 200 gp for spell inscription costs as well...)
Or, to save on money, someone could spend the time for reverse engineering the spell, and then learn the actual spell next time you level up as a Sorcerer or Wizard without paying the gold pieces, since new spells you learn every level are apparently learned by doing research between fights......
As for the Druid with Natural Bond thing, the short answer is no.
The rules as written could be interpreted to say that you can, BUT, it's a rather poor way to interpret it. Even though your level isn't increased for determining your monster's bonus stats, you still have more than your character level in effective druid power because you are using a stronger monster than usual; it's a bit like taking a feat to completely ignore your Level Adjustment. Plus, druids are strong enough and don't need the help.
I will let you change Lucky over to a riding dog, if you want, since you can just summon a new animal companion any damn time you want anyway. Bonus RP points for doing it when you level up, so that it's more like "I did some retraining and got better so now my animal companion (who is linked to me) is better too" than "I got a new dog which is just like the old dog but better".
Also, if you really need to buff out your dog, get him some magical bling. Animals (quadrupeds, anyway) have the following body slots available:
-hat (not helmet or headband, but hat)
-cape (not applicable if the animal wears a saddle)
-Amulet (or brooch, medallion, necklace, periapt, scarab)
-Bracers (not bracelets)(unlike most Magic Items, these won't resize properly for animals, due to the different leg structure, and must be specially made)
-belt
-booties (also must be custom-made)
Note that if you put all of these thing on your dog/cat/horse, he will look SILLY.
Do you see how silly this dog looks? Your dog will look even sillier.