I have mixed feelings on this. Some kids are ok with this while others, age 4 is just too young. Kids that young really aren't ready for organized team sports (I do realize there MAY be exceptions). I also think that starting kids too early and/or pushing them too hard can do more harm and discourage love of a sport by taking the fun out of it.
Here's my experiences:
My son was 4.5 when we moved and he had missed soccer sign up (he had never expressed an interest yet) so when he started K and his new bf was playing he wanted to play. It was too late for that season. But, at age 5 he started wrestling, then t-ball, and later soccer. He continued all through 9th grade (taking his 7 & 8th grade years off from soccer and trying football), then he simply dropped baseball and continued w/ soccer and wrestling. They were great fits for him. Our rule was ALWAYS that he didn't have to sign up for ANYTHING but once he was signed up for it (whether it was for the month, the season, or the year) he was committed for that time frame...if he didn't like it he would not have to sign up ever again. He became an Eagle Scout too.
My daughter is 6.5 right now. She has never expressed an interest in signing up for sports (even when asked) but is very active. We did sign her up for a "sport skills" camp that was for 3-5 year olds for hand eye coordination (nothing too structured...just fun). She also did two separate summers (1 x per week) of different fun-themed dances (age 4.5 & 5.5). She enjoyed it but didn't want to sign up again (until the next summer). She enjoys singing and signing w/ a few other kids at church (they only practice for a few weeks then perform and then take a break for a few months). She did want to sign up for Daisies this past fall and has already asked to sign up for this year. She's not ready to participate in "organized sports" but is more than ready for a variety of experiences.
My nephew is the same age as my daughter and my sister signed him up for winter soccer the very first year he was eligible (age 3). I watched a game halfway through the season, only one or two kids on the whole field really seemed to be into the game and actually trying to play. The coaches and parents that were helping had to keep reminding the kids to go after the ball. I think they should have maybe focused on soccer skills rather than having teams and playing games.
You know your daughter best so if you think she is ready, sign her up. I suggest before you do, you and her dad get on the same page about completing the season if she wants to sign up.
**For those that say this age doesn't know what following through on a committment means, they are right. That's what us parents are for...they don't know what ANYTHING is until they are taught it (whether it be through observation, reading, a teacher, a parent...however).