Under technicalities, Family Matters and the Urkel character were spinoffs from Perfect Strangers.
Harriet Winslow worked in the same place as Larry Appleton when he was working at The Chronicle. She then got her own show with the handsome Reginald VelJohnson (who might be gay) and the Urkel character came into being. By the end of the series run, Urkel had become something of a cartoon as had most of the cast and story lines (thanks to poor writing at that point), so technically, there's a Perfect Strangers cartoon spinoff and Urkel is a cartoon character.
But do you really want to go to that series? Look at the problems.
Reginald VelJohnson would be against all your beliefs.
1)he's been said to be a homosexual
2)he is said to have attended high school with porn star Ron Jeremy.
Then again, George Tenet also went to the same school (Benjamin Cardozo), there could be an interesting story where Urkel in his Urkel cape is trapped on an island with Carl Winslow and porn actor Ron Jeremy and the Skipper (no Ginger or Mary Anne or Gilligan) and the Harlem Globetrotters (who had their own animated-cartoon series). As the skies turn ominous and the waves churn the small island they are on seems destined for ruin.
Nearby on a similar island which is cloaked by a Romulan cloaking device, George Tenet and his staff are planning how to unleash a swarm of tickler mosquitoes on an unsuspecting underground nation. Drac Cheney is visiting to have his hologramming abilities restored. A flare shoots into the air and an image of Urkel appears. Tenet and his crew of men and women know there's danger and leap into their invisible magic manatee ship and head to the island where they rescue the stranded men. They return to the mainland and all is well as the credits roll.
Next week, Urkel and his nerds take on Lebanese bureaucrats.
You think there should be a series, then make it happen.