Yes it's within capabilities if you're fairly savvy, they're not that difficult judging by my DIY experience of changing mine. Remember fitting a DIY system probably won't be recognised by your insurance company tho, if this is a consideration.
Inside the control panel there'll be a 240v power feed, and probably a battery back-up. There'll be a pair of wires going to each zone, some wires going to your keypad (assuming you have one, I don't "know" panels and it won't let me enlarge your picture), output wires for your internal speaker/horn, and for your external siren/strobe, and it might also be connected to your phone line if your panel has that function. You might choose to connect your new system to your phone line?
AFAIK most systems work on 12 volt DC, and the only parts which need to be compatible are the control panel and the keypad. All the other existing sensors/siren etc can be programmed into your new system. It's really a case of noting down (and understanding) where the old wires come off, and where to fit them on the new panel. Therefore I reckon any panel/keypad combo you buy will be compatible with your existing system. I went for a new panel from the same manufacturer as my old one tho, maybe it made it easier, maybe it saved me some time messing about with tamper resistors etc, maybe not?
Some (maybe most?) alarms have a siren which will sound when tampered with. They work by being constantly fed a "hold off" power feed. If yours is like this then at some point during your disconnection your siren will sound until you remove it from the wall and figure out how to reset it, or until it's own internal back-up battery has drained, (or maybe you could somehow feed it a temporary hold off?). It might be an idea to start here - figure out how to silence it.
Regarding choosing a new panel I have found that some systems have a speech/text dialler in-built so it calls/texts out if the alarm is triggered. Beware that some of the more professional units are really geared towards contacting an Alarm Receiving Centre (ARC) like ADT etc for a monthly fee. Others, however, are more geared towards phoning/texting you, the owner. Do a bit of homework and get a panel which does everything you want it to.
Hope this limited info is of some use