Get her hair trimmed at least, to get rid of any dry bits.
To be honest, short curly hair on a toddler might be more of a pain than long hair.
My DD has lots of coarse, curly hair, and over the years I have found it less of a faff (still a faff...but less so!) to do the whole wash, condition, comb and then plait thing than to deal with a crazy, curly bob that is too short to be put up off her face (loose hair is also a nit magnet in that age group, I find!).
Can you braid hair? Would she sit in front of CBeebies for a bit while you did it? I braid my DD's hair on a Sunday night and it lasts a good few days if its done fairly tightly with product in it.
General tips for dealing with curly hair:
Dont wash it too often.
Dont brush it when dry.
Condition it really well!
I use a very gentle shampoo on DD's hair on a Sunday, slap on loads of conditioner, comb through while wet and conditioner soaked, rinse, tangle teaser it again, then blot with a towel very gently and style (plaits usually).
If I need to restyle during the week, I wet it with a spray bottle of water and put a leave-in conditioner in it before I go near it with a comb.