Can you walk us through what exactly you expect to be able to do with this antenna? Like, where you will use it and what kind of signal you'll see with it exactly?
I have a fair bit of tekbox EMC gear now that I use for precompliance testing, because they're good bang for buck - but I don't have their antenna because even though I've considered it a few times, it's not going to do much that I need.
At the end of the day, unless you have a good and complete setup for measuring with an antenna, anything you catch with even a calibrated antenna is unknown, because:
1) Add in unknown reflections and resonances in the space you're working in, and then the calibration of the antenna becomes irrelevant... so you need a calibrated anechoic chamber or an OATS. not a regular electronics lab.
2) With no isolation from the rest of the world, you'll spend an awful lot of time turning stuff on and off in order to try and work out what's even your DUT, and what's just crap in the environment. (actually that happens in anechoic chambers I've been in, too.. just not so much)
And that's why the internet EMC experts don't tell you to buy thousands of $ in antennas for a basic DIY test setup.
Neither of those antennas from bunnings or rfshop look that great to me for EMC purposes.. you don't know what their operating range is even meant to be
OK you can guess, 700MHz to up past 2.45G for the rfshop one, based on what they say it's goot to use for, but can you be sure it has no bad blind spots where it's deliberately filtering out bands that aren't of interest to its purpose as a radio signal antenna in order to make it more interference proof? at least the tekbox antenna basically gives you that whole range it's specced for.
I'm not even sure what to expect from a digital TV antenna with an amp like the bunnings one...
Does your spectrum analyser have a tracking generator? if it does, you could buy two of these rfshop antennas and set them up maybe 5m apart in a football field, pointing right at each other, polarised the same way... maybe with an rf amp to drive the TX antenna for better noise immunity (watch out for breaking rf regulations!) then you could try to run sweeps and measure the frequency response of them as a pair... assuming they are each responding the same way (Tx response same as RX response) then you might infer a frequency response of those antennas?
But if you want to do that, I'd probably start instead with a handful of doubles of the log periodic antennas from here...
https://www.wa5vjb.com/ they are probably close to what's actually inside the aaronia LP units... but with no calibration or nice housings or anything else.