I like Dave Ramsey's ideas on this -- in fact, "Financial Peace Junior" is what I had my mom get my boys (3 & 5) for Christmas this year. We've read some of the books, but haven't started with "the program" yet -- I figure once we get back into a routine with the New Year we'll start.
Basically, he doesn't like the term "allowance" -- it's too much like Welfare, where you get money simply for existing, which doesn't work in the job market. In the real world, if you do work, you get paid; if you don't work, you don't get paid -- he thinks children should learn those principles. To do this, you establish certain chores that they need to do around the house (obviously, with starting out, especially with young children like yours and mine, you'll have to do a lot of hands-on time, doing half the work yourself, as "they" clean their room or whatever). But, there also needs to be things they do without getting paid, just because it's the right thing to do, and builds character.
An example of a chore chart would include something like feeding the dog, or loading the dishwasher every night (obviously, for older children). Each chore earned them a certain amount (like a dollar), so if they did their chores every night, then at the end of the week, they would get $5. If they didn't do a chore one day, they'd only get $4. But if they shirked their duty several times that week, they'd get some form of punishment, because they starved the dog. There was a minimum amount of effort they needed to put forth, "just because I said so," and if they let too many of their chores slide for too many days, they needed to be put right.
How much to pay depends on your own financial circumstances -- a single mom with 4 kids won't be able to afford the same pay scale as someone making 6 figures with 1 child. As a SAHM married to a teacher, we don't have just a ton of money, so my children definitely get on the low end of the pay grade... but then, I'm training them to get stuff at yard sales, and a dollar goes a lot further there, than at the store.
In "The Tightwad Gazette" books, the author did not give her children an allowance, and said she paid them "slave labor" wages (not above $1 per hour). However, that was almost 20 years ago now, when minimum wage was probably still about $3-4/hr, so you might want to increase that standard a bit. ;-) But, basically she would see how long it took to complete a task like taking the compost bucket out to the compost pile (they had a large farm with plenty of chores available to do), and if it took 5 minutes to go out and back, then three trips earned the child a quarter. But she didn't pay them for everything they did -- some things were done just to pitch in and help the family -- she noted one time that 5 of her 6 children cheerfully worked together with her canning vegetables, without expecting remuneration (the 6th child was helping her husband with a task).
The good thing about starting as young as you are, is that your daughter still probably thinks everything is a fun game -- take advantage of that! Turn "chores" into "fun time" and then pay her money (my kids would rather have 5 pennies than 2 quarters, because "5 is better than 2" -- I'm gonna have to work on that!) according to what you can afford, and how difficult the job was, and how diligently she worked. But, yes, start now!
What sort of chores? Depends on what you have to do in the house, as well as your child's aptitude and attitude. You may or may not want to pay her for cleaning her room, if that's something you think falls into the category of "you're a member of this family, so you need to do a minimum amount of work in this house". But you can start working with her now, teaching her how to sweep and vacuum floors, fold towels and other simple things, separate her clean clothes from yours and perhaps put them away, etc. Try to find things that she will think are fun to do, at least to start, to get off on the right foot.