Go for something gentle on all of you...
As a veteran of carrying small children for up to a mile at a stretch on numerous hikes... I would advise going for something easy on all of you. Obviously, you want to avoid open slippery rock ledges, and probably anything with extended, trippy, rough, rooty sections, at least till you have a sense of how you do together.
One easy trail I have done recently (amounts to a "walk in the woods" for the most part) is Greeley Ponds Trail from the Waterville end (Lincoln side is steeper and rougher). You get a nice walk in the woods, a beautiful view, and nothing too strenuous. Another option might be something like Sabbaday Falls or Lincoln Woods.
Chances are, at four months, she's like luggage without a handle and, as long as you avoid anything rough that might result in a trip-and-fall, you will both have a great time -- you get to be close, she gets constant motion and visual stimulation. Have fun!