An AQM-34L desktop model exists in approximately 1:32 scale (11 inch length, 5 inch wingspan). The manufacturer is not known, perhaps it was made in-house by Teledyne-Ryan? It is a single piece solid resin casting. Apart from the version without markings, two versions with markings were offered on Ebay. The first is L229 / Tom Cat and the second L161 / 'Brit Special' with 'Col. Ray P. Britton' on the stand (the latter likely a leaving gift).
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An AQM-34N desktop model with many similarities also exists. The stand is in the same style, as is the name plate on the stand. The model is approximately 1:30 scale (11.25 inch length, 13 inch wingspan). The nose piece is likely missing on the model shown.
An AQM-34Q/R desktop model was offered on Ebay in August 2010. My best guess is that it is a conversion of the AQM-34N model shown above, fitted with drop tanks and a 'football' radome on the fin tip. The model likely represents a Model 147TF / AQM-34R. The Model 147TE / AQM-34Q has a cilindrical UHF antenna probe on the radome, that the model lacks. Instead it should have a small blade UFF antenna just behind the radome, but I don't see that in the photos. The dimensions are reported as 11 3/8 inches length and 12 7/8 inches wingspan, which agrees closely with the AQM-34N dimensions. The stand lacks an identification plate.
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Craig Kaston found a BGM-34C desk model in the collection of the Pima Air & Space Museum. Craig points out the almost full span ailerons and the trailing edge root fairing, along with the full height rudder. Under the wing are ALE-38 chaff pods.
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John Nitka kindly provided photos of 1/28 scale models by Topping Incorporated. On the left is the Air Force Q-2A, on the right the Navy KDA-1.
John Nitka also provided a photo of an BQM-34A / Q-2C model by W. Osgaard & Co Models from Denmark (left). On the right are two similar models of BQM-34A's in aluminum, found on Ebay.

Former Teledyne-Ryan engineer Ray Vitkus (see his photo page) also has a collection of desktop models. The left BQM-34A Firebee is fitted with some kind of wing tip pods and shows remains of 'US AIR FORCE' on the fuselage side. Ray reports that both the radome and the parachute cone are removable. The right BQM-34A Firebee has correct tail surfaces (including dorsal fin on the parachute cone) and the correct wing cross section.
Offered on Ebay was this plastic model with 'BQM-34A FIREBEE' and 'BB' logo (from Ryan Builds Better) on the base. Dimensions are 9" length and 5 1/2" wing span. The manufacturer is not yet established, but considering the similarity of the metal model below, it could be Fermo.
Again found on Ebay is this desk model of the Firebee I, painted orange with black tips. It measures 2.75" / 70 mm length and 1.75" / 44 mm span. The length suggests a scale of around 1:100, but the wing span does not agree.
Ray Vitkus owns this model of the supersonic BQM-34E/F. The manufacturer is not yet established.
Also offered on Ebay was this plastic model with 'XBQM-34E FIREBEE II' on the base. Dimensions are 11" length and 4" wing span. The manufacturer is probably Fermo (Osgaard ?) - compare with the BQM-34A models shown above.
An identical model was offered on Ebay, this one having the 'BB' logo (from Ryan Builds Better) on the base. Reported dimensions were 10.5 inches length and 3.75 inches wing span.
Also found on Ebay is this desk model of the Firebee II, painted dark red with black tips, and measures 3.25" / 83 mm length and 1.5" / 38 mm span. The length suggests a scale of around 1:100, but the wing span does not agree. It appears identical to the Ray Vitkus model shown above.