One of the jokes played in 'Eureka' on Feynman's Day (May 11) this year had Global Dynamics office drone Larry as the target. He was left with a high-pitched squeal of a voice. Zane Donovan told him to relax, that he would be "de-Beakered" in a few days.
In Toobworld, puppets are alive (for the most part.) They are spirit beings who take on the characteristics of the shells they inhabit. So Kermit would be a frog for all intents and purposes. Chairy would be a chair; Miss Piggy would be a pig; the citizens of 'Lidsville' would all be hats.
(Some characters we know to be portrayed by puppets are not - 'Alf' and Rigel of 'Farscape', for example.)
As for Beaker? He's a puppet shaped to look like a science nerd.
Zane may have known about Beaker if the Muppet Labs employee was ever invited to be an intern at Global Dynamics.
Or maybe Zane saw Beaker on 'Muppets Tonite!' (That was a TV show, available to be seen by everybody. 'The Muppet Show' took place in a theater - to have seen anything that happened on that show, a Toobworldling would have had to have been there in person at the theater.)