Take time to enjoy it! You don't have to see everything, ride everything, experience everything. Don't put unnecessary pressure on yourself.
I would however make the most of your experience, don't ride something on one side of the park and then run to something on the other side, it wastes time. I always take a "path" and follow it, for example: up main street, into fantasyland, loop around to Matterhorn, it's a small world (I skip toontown for the most part. There are some great photo ops and character meet and greets but the rides leave something to be desired IMO then around to Tomorrowland, across to Adventureland, New Orleans Square and Critter Country.
Also, FASTPASS FASTPASS FASTPASS. One of the first things I like to do is grab a Fastpass that I won't use until much later, and grab as you go around.
Trying to see and do EVERYTHING in a Disney park is like trying to eat a really, REALLY rich dessert way too fast! Pick the things that are most important, and focus on those.
Also, don't forget the smaller, non-thrill ride things, as they may be the most memorable and enjoyable, such as the riverboat or Storybook Land.
You'll hear a lot of people with STRONG opinions on different attractions - what's good, what's bad, what should be removed, etc. However, for everyone who loves something, you'll find someone who hates it, and vice versa. Listen to opinions, but take them all with a grain of salt. Don't let anyone discourage you from anything. It may turn out to be your favorite.
Also, depending on your daughter's age and temperament, if she doesn't want anything to do with the characters, don't force her. Some kids, like one of my daughters was terrified of the characters. Her older brother and little sister never were. Each kid is different. But no picture with Mickey Mouse is better than a picture of your daughter screaming in terror at Mickey.
Take lots and lots and lots of photos because you are after all making memories that will last a lifetime, and you wanna be able to look back on those memories in photos! besides this is your kids first time, so take lots of photos!!!! that is the only tip i can give, other then use the Fast Pass system.
My #1 TIP is to ASK QUESTIONS and to ask different cast members the same question.
"How do we....", "Where can we....", "What time should we...", "What is this..."
People miss out on a lot and have bad experiences because they assume stuff. They assume that an attraction is closed because there is no line. They assume that they have to go a certain way when a Cast Member will know a quicker, better way. They assume that they have to wait for the whole parade when a Cast Member will direct them to where they can cross the path. They assume they can get somewhere right when something starts when reality is a Cast Member would have told them to show up 45 minutes before hand.
touringplans.com is worth the couple bucks for membership! They have great touring plans, and give you a good idea of crowd levels so you can plan accordingly.
THIS! 100 times over. I've been to disneyland over 100 times and went yesterday using one of the TouringPlans.com plans and I experienced more of the park in one day than I have in a LONG time, and it was BUSY yesterday but I hardly noticed - I think the longest I waited in a line was 30 mins. Worth. Every. Cent.
Start with a complete ride around the park on the train. Its a classic, will tease the different areas, and is just a great ride. Its my starting point on every trip.
I agree with this too!
Also, you know your daughter, pick rides and shows according to what you think she'll like most. Since we don't know her age it's a little harder to comment but use fast pass where you can and where you can't, if the line is too long (over an hour) try to go back to that ride at night a few hours before closing....the wait time will definitely be shorter. Like Matterhorn.
try to watch Fantasmic! and/or the fireworks because Nobody does fireworks like Disney.
And don't forget to stop and rest. I am so guilty of this even though we go so often and I will still find myself being beat and sore because I'm always "go-go-go". . This can even be achieved by sitting and waiting for a parade or getting on a slower, relaxing ride such as the Mark Twain or Pirates.