u/HasturFhtagn — reddlx

Or some other creation of Rick's. I've always thought she acted out-of-character in this episode, but on rewatching, I think she actually just might not be real.

At the beginning of the episode, Beth mentions that she had a cancellation and has invited them in for a session. It's a sudden thing, not part of her usual schedule.
Also at the beginning of the episode, Jerry is finishing up his last therapy puppet, a project he's presumably been working on for a while. Beth thinks it's dumb, but Rick doesn't mention it. In fact, he specifically manipulates the situation so Beth and Jerry go to therapy and the kids don't.
At therapy, everything Dr. Wong says is wildly out-of-character for her. She calls Jerry and the puppets dumb and crazy, and when he points it out she just deflects with some slick comment about the British Baking Show. It's played off as a joke about how dumb Jerry is, but none of it seems like something she would say. It does, however, seem exactly like something Rick would say. She even more or less uses Rick's inflection.
When Rick actually gets there, he specifies that his guns should "whitelist human life...and the therapist". Again, it's played off as a joke that he doesn't consider therapists human, but it could well be literal. It's not like he specifies "and Jerry".
When she does actually speak to Rick in person, she only says basic therapy-speak lines about how he's booby-trapped or blown up her office. Once again, played off as jokes, but when Dr. Wong speaks to him in other episodes, she nearly always has something meaningful to say, and she nearly always gets him to listen even if he doesn't want to or is otherwise occupied. He doesn't even really take time to insult her, he just kind of dismisses her and moves on.
It also fits with the episode thematically. This episode is the introduction of Space Beth, and the main philosophical theme of the entire thing is about Rick's ability to create life and his general refusal to care about it. A background character being artificial also would fit in alongside that.

Why would Rick do it? Because he thought the therapy puppets were annoying, and this was the best way he could think of to get Jerry to shut up about them.