I had the same problem with my four year old and was surprised that just letting her pick out an expensivea new colorful pair of running sneakers to "go super fast" was all it took to get her going much further without me carrying her. Maybe I just lucked out, buy you might try making a big deal out of a new shoe purchase.
Another idea is grab another kid to go with you. I have twins, and often they run ahead together too busy to ask for me to carry.
Or another idea is try having everyone in the hiking group take turns being the "leader". You follow your daughter when she is the leader, and maybe take turns.
Having your daughter pick a hiking spot and having a goal in mind also helps. Having a physical book (like this one) with hiking trails in your area with lots of pictures helps a lot. She picks a hike, and then is excited to go there and find the spots in the pictures. It also helps if things have fun names like "Rainbow Lake" or if you use your imagination and say look for the big black fish in the middle of the lake as we hike.
Be careful not to push her too hard or else you'll risk making her hate hiking completely.