Yes of course :)
In June, we took our 18 month old to Bologna and stayed in an apartment. We explored the city and used trains to go to Ravenna, Rimini, Ferrara and Padova :) He uses reusable nappies and washing them was no issue either.
It was no more difficult than carting him about in the UK and we had such a good time that we booked another holiday to Spain in September :)
We've never been 'sit on a beach' sort of people so I can't speak for that kind of holiday but a city break with a toddler is great fun.
Tips:
Snacks: Find a supermarket and buy snacks! Sometimes if our son was getting cranky then whipping out a bag of rice crackers was enough to keep him busy.
Travel buggy: Get a good portable buggy that folds small. We have the Ickle Bubba Globe and it's amazing. It fits in the overhead locker on a plane so you have it as soon as you're off the plane. Lots of people rave about the YoYo but it doesn't lie flat for sleeping whereas the Globe does. It's also about half the price and you can pick them up second hand too.
Travel cot: We bought a second hand Baby Bjorn travel cot on eBay and my god is that thing light weight and easy to use. Having a familiar bed is great for helping sleep in strange places. A portable blackout blind is great for this too.
Travel highchair: We got a foldable booster seat with straps so we didn't have to worry about finding a high chair as it just clips onto a dining chair :)
Toys: Little portable toys are good to bring too. Our son has a 'lacing cheese' (Google it, I love it 😂) some wooden stacking animals and blocks for the apartment/hotel room, little board books and buckle toys.
Be adaptable: We have strict routines for our son at home but these went out of the window when travelling. He ate and slept much later but it all seemed to fall into place naturally :)
I hope you have a brilliant time away! :D