Moose and Zee are pretty awesome. I'm also a huge Wonder Pets fan--they do a good job of keeping it non-annoying. Absolutely can't stand Wow Wow Wubzy. It's basically a poor toddler's version of Spongebob Squarepants. And a theme song that will stick in your brains for days...
As far as Wonder Pets go, I've tried to think how Linnie/Tuck/Ming Ming relate to Trek's beloved Big Three. They really don't, because Linnie, who's the "captain," is also the most logical one. Tuck's all about compassion and observation, while Ming Ming's impatient. So they don't really line up well with Kirk/Spock/McCoy.
I wouldn't be totally surprised if they rescued a baby Gorn someday, though.
And you probably don't really get to know this stuff until you've got to watch it with someone who will scream if you change the channel at the wrong time. You learn pretty quickly what you can tolerate and what you can't.