Since you will be on vacation.... I would bring a stroller. Vacations usually entail LOTS of time walking around, sight seeing, standing in lines, or in the hot sun, and a young child will get tired, and their legs will get tired too. And they will be in a different time-zone.
Their stamina is different from an adult.
Her own suitcase to pull-around herself- do you mean a carry-on bag type thing? Or to pull around while you are there sight-seeing or whatnot? All I know is, when a toddler is tired, and there is a lot of people/crowds or whatnot, they get tired/fussy of pulling their own bag. AND her pulling her own bag around, will slow her down as she will have to navigate herself & the bag around the people/obstacles/crowds. So you might end up having to pull it around, for her.
At this age... they are not fully able to manage carrying a load of stuff... maybe just a small back-pack (nothing heavy) to put around their shoulders.
I would, bring an umbrella stroller type stroller for her, just in case. When my kids are tired, and even just all day running errands and walking around a lot or in a crowded area or sight-seeing, they even like to be in a stroller. Or, we just have to stop, and rest, or they nap.
Your toddler, may even end up falling asleep/napping in the stroller too... especially when you are all out all day (which is typical when on vacation) going here and there.
All the best,
Susan