Lots of good advice up there, but it's such early days your DD will have plenty of time for other sports, brownies, play dates etc for a good while.
My DS started competitive swimming when he was 8 and is still competing and improving at age 16. He got his first pair of fancy jammers just a few weeks ago - he really wasn't all that bothered about having them, and he has always thought that you'll gain more advantage by having a great start / turn / finish. He is regularly swimming at nationals, and has recently joined a sprint squad so no longer has to train such long hours covering 1000s of metres each week (down from 16 hours a week to around 6) making school work / social life / swim training a lot more balanced.
My advice is to get involved with the club, clubs are run by volunteers and you'll get a lot out of helping - squad rep, kit, fundraising, helping at galas, timekeeping or judging, helping poolside etc. Get into lift shares if you can too. Keep an eye on clearance sales on the main online swimming kit providers.
Your coach will guide you as to which meets / events to enter (you need to be 8 to compete at accredited meets), for the younger ones it should be about having fun and swimming as a team - plenty of time to get serious later on.
Remember that there are many ups and downs along the way - long periods when their progress plateaus and there doesn't seem to be any PBs - and keep positive and focus on what they do well and encourage them. Don't live your life through them - competitive mums / dads are truly cringeworthy!