I love doggies and underdog is my favorite superhero
I guess that nobody at Marvel ever considered this crossover. However, they'd need permission to use Underdog. That's not to say that it couldn't happen if the fans asked for this. After all, the Punisher was actually in an Archie mini-series a few years back.
He is too silly for such a serious team
Because he's not a Marvel character, so they can't use him.
Different Publishing company.
Besides, The REAL Avengers are Led by "Mother", and work for the Ministry, (remember John Steed, Kathy Gale, and Mrs. Peel, and then came Tera)