You might want to read the article on sizing fly rods to body size at ... http://flyanglersonline.com/
Some fly fishing clubs put on youth schools ... my club puts on several each year ... one is for members only ... they teach the kids about casting, fly tying and equipment.
Read/look at together a copy of the "Curtis Creek Manifesto" great book for beginners.
Also, if you are going to fishing apart in a river (a mistake) ... make your daughter stands up stream (so you can catch her as she floats by) and give her a new fishing vest (Sterns Life jacket with pockets). I did these things with when teaching my son, it will help your peace of mind in the river.
A hat, sunglasses and barbless hooks are also all good ideas for safety.
A six year olds attention span is short, so be ready to look for snails and crayfish ... skipping rocks ... a little swimming ... and then ice cream. The real key in the beginning is spending some one on one time with Daddy.
Don't think you will get any fishing time for yourself ... tying on flies and untangling lines will take up all your time. Oh you can take your rod ... so she can fish while you fix her rod ... then by the time her is fixed ... yours will need to be fixed and so on ...
Juro is right ... Blue gills are the game fish of choice to start ... in a lake ... not a river.
In a few years your daughter will have a better casting stroke then you, out fish you and love the sport ... you will know then you did it right ... Good Dad!