The above posters are correct that you have a bike that you can use for Audaxing. However, there may be one or two changes that you can make to allow a more comfortable riding experience.
1. Change of Tyres.
Part of the effort needed to ride a bike is attributable to the rolling resistance of the tyres. You may therefore get some good benefit from changing your current tyres to something lighter with less rolling resistance. A quality tyre is a good investment so something like a Continental Urban in 35c, or even a Continental GP5000 in 32C or 28C. There is lots of choice but if you want to be overwhelmed with information take a look at
https://www.bicyclerollingresistance.com/.
2. Change your innertubes.
Again, related to making the wheels go around easier, you could change your inner tubes from the rubber ones you currently have to the newer type of TPU.
3. Handlebars
The straight(ish) bars fitted to your bike don't give many options for hand positions. If you don't already have something similar, swapping your handle bar grips to something like Ergon grips would be good as this type of grip is much more supportive to the hands.
4. Are you sitting comfortably.
This is about getting the sadlle position and stem length correct for your style of riding. Refining your position as you get fitter will minimise the aches and pains you get from sitting on a bike for extended periods. A 200km Audax ridden as 20 kph will take 10 hours! Have a read of
https://wheel-easy.org.uk/wp-content/uploads/bike-set-up-2017a.pdf5. Practise for 'mechanicals'
When you do longer distance rides your are more likely to run into minor mechanical issues. I'd suggest getting familair with two activities.
A. Replacing inner tubes (don't faff around on Audaxes mending punctures. Take two extra innertunes with you to swap in if you get a puncture. Mend punctures at home in the warm whilst indulging yourself with a nice cup of tea and a bit of cake).
B. Adjusting the indexing of your gears so that they run smoothly.
6. Get some decent quality cycling shorts ( and some chamois creme)
A decent set of shorts will fit comfortably without and rubbing (small movements of material around your sitting area). Even so you might benefit from applying chamois creme as your rides get longer.
7. Saddle
Be prepared to discover that the saddle/bum interface is not good for longer distances and that you will need to seek out a different saddle as the distances increase. Saddles are very personal things so you will need to do some research. Good saddles to look at initially would be the SPA Nidd or Selle SMP TRK. You say you already have a Brooks saddle but this type of saddle doesn't suite everyone and is also not the best type of saddle for the design of bikes you get today (seat tube angles and all that). A common problem with Brooks saddles is that it is not possible to move the saddle back enough to get to your optimum bike position.
8. Finally
Many people make the mistake of buying an Audax specific bike too soon. I'd suggest a year of Audaxing on your current bike (with minor upgrades) before you make a purchase.
Have fun