What's your budget, and do you have any constraints re: storage space for the trailer?
(do you all others think a guitar would be able to lay flat in a kid trailer?)
I don't have any hauling suggestions to add to the above, but bringing a typical amp for practice every week may be overkill. I've taken some classes at Old Town School and use the amp below. Weighs 1.5 pounds, powered by a 9 volt battery, not much bigger than a couple paperbacks and enough sound to practice with. This one is a Fender at around $40, I'm sure you could other similar options.
This is NOT my bike, but it's exactly what I did to my 90s Fuji mountain bike. It can easily cart a guitar and probably the amp too. Depending on where you live and how convenient it is for you, mine's sitting in my apartment or garage and not getting used enough. Message me and we can most likely work out a way to share it for the days when you need to cart your gear. You can also carry your bike on it (especially if your front wheel comes off, that's easy) so you can bring it back and ride yourself home :)
Or, invest in an xtracycle yourself. They're amazing! (I got mine, used from a fellow chainlinker.)
My favorite commercially available trailer by far:
Here's my cargo run yesterday:
The suggested size is 36" x 24". I have built several at 48x24", but the one pictured was built to transport a specific instrument case and is 30" x 24". Stroke of luck that the carton I had to pick up from fedEx fit perfectly within the eye hooks.
Also fortunate-- the roll of carpet went limp after a couple miles but never sagged all the way to the ground...