I would highly recommend an endfed halfwave antenna kit.
K6ARK makes a nice halfwave transformer kit for about $30 that will handle the power levels of the QMX easily and is not much larger than a BNC connector.? You can also roll your own 49:1 transformer easily as well, but the K6ARK kit is hard to beat for form factor and not expensive.? Just adjust the radiating element for 40/20 or 30 - I have an "extension" on my antenna that is a couple ring terminals and a nylon nut/bolt that I use to add length to my antenna for alternate bands.
For batteries, a small 3s drone battery with a low voltage beeper alarm is light, small, inexpensive, and very dense power storage.? You should be able to get a decent battery, charger, and accessories for well under $50 and possibly even in person anywhere that sells drones or RC gear.
Let me know if you have questions, I can bust out my kit and take some photos!
What part of Ireland are you in?? I went to visit some time ago and spent inordinate amounts of time enjoying the trad music scene in county Kerry - It's beautiful countryside over there!
-N1EDC
