No, its a real North American project called Rapier - or "Lightweight Air Superiority Fighter" in this case. Photos of a model of it owned by Sir George Cox is in American Secret Projects. I've added some pictures from Tony Buttler posted previously.
I'd venture an educated guess that this design was entered into the late 1952 GOR for a lightweight air superiority fighter against the Lockheed L-246, Republic AP-55, and Northrop N-102 Fang, that resulted in the F-104.
Published sources have said that North American submitted the NA-212 (F-100B/F-107) but this project seems too late to fit the timeline. Lockheed's L-246 won in Jan 1953, but NA-212 started development in August 1953.
Additionally, the shape of the design looks appropriate for early 1950s and the size of the model fits this competition better than anything else I can think of. It might be a private venture model perhaps, but mid 1950s at latest.
Model is 28cm length and 18.6cm span. At 1:32nd scale, that would be 8.96m length, 5.96m span. Pretty much in the Folland Gnat category. Judging from the relative size of the canopy, I would say this seems about right.
1/32 scale seems most probable; if it was 1/48th the resulting airplane would be too large, 1/24th scale too small.
First, it did come after the F-108, because it was known as the Rapier II (please revise topic title accordingly).
Second, here is an illustration showing how the rockets are launched in orderly fashion, while the engine cleverly refrains from ingesting any gases.
Third, there was an NAA Rapier III (saw it mentioned in a report), but I'm not sure what that was.
2 photos of a wooden inhouse "Rapier III" model are on P.112 of Secret US Proposals of the Cold War by Jim Keeshan. Single engine, longer than Rapier II, something like a blend of Rapier II with an F-100B. USAF markings.