Maybe a loop antenna would be best for you.
A HF dipole could be huge.
Lower HF antennas are large enough to make rotating them difficult at best. Would you want a helicopter parked in your back yard, with its rotating blades. A dipole might approximate that.
Calibration? I would expect them to vary significantly with orientation and height.
For a stationary antenna, and a single, fixed direction, You might be able to extract the parameters with a VNA, at a fixed interval, say 1 MHz, and then use a spreadsheet to apply a correction factor "mask"-like over the raw DUT measurements to get the corrected response.
I suspect that would only work if the impedance was constant and known, which is unlikely, though.
These antennas are for 100 MHz and higher, I am looking to work out how to calibrate a small dipole for use on lower HF frequencies.
But thanks
The dipole likely will have a smoother response if you use the special balun which they use of biconical EMC antennas.
I don't know if you can approximate a biconical antenna with what you have, but I have attempted to build a great many broadband antennas in a repeatable manner, and I can assure you that the response of a vertically polarized bowtie or biconical or planar disk antenna (the last one, mentioned by Laser Steve above, is a particularly easy and useful antenna, and very easy to construct, using two conducting circular disks, like pizza pans, and a stick. It eliminates the need for a balun if you properlyground he shield to the bottom, but it is finicky. You have to do it completely.
You could try a horizotal "bowtie on a stick" like that of T3sl4co1l Tim, above. - that bowtie shape I think could give you a more manageable antenna for any given frequency, size wise. Shortening its wingspan by at least 25%
With his or another balun, (i'm attachinga design below, this might work well, set to the 1:1 setting. It is likely to be much more broadband than any dipole you'll ever be able to make. Try it. Its a good start. Youre unlikely to find a way to fit more "antenna usefulness" into the space. isnt that usually the challenge?
Its not impossible to get an antenna that works over a 10:1 frequency ratio. 100-1000 MHz is not that difficult. And the construction is much easier than a discone. Make sure to use a balun,if you feed it with coax you'll have to.
Amplified active broadband e-field antenna.
As far as an e-field antenna, there you can utilize something like a mini-whip high impedance amplified antenna.
https://circuitsalad.com/2020/02/13/simple-low-current-mini-whip-antenna/it will give you a good VLF antenna in a small space and may perform surprisingly well if you get it far enough away from your house and its noise field. It works on capacitance.