A visit to the gym is going to be different than what will happen when you decide to find a great caregiver or preschool. That teacher is going to be your partner in helping your goodbye transition with your little girl. That teacher is a person she will have met before, because you'll visit together, and someone she will develop her own relationship with. She's going to have to learn to trust another person besides mama.
Venturing out and then touching base is what happens a lot at this age, so don't think this is anything to worry about.
I'm a preschool teacher who's also been a toddler teacher and I've worked with little ones for nearly 20 years. I try hard to work with each child when they encounter this grief at separation; some kids need to be held and have their feelings affirmed; some kids need a place to sit alone and to come to the group when they are ready. That said, in regard to readiness, this isn't something you can practice-- you just have to do it.
Often, too, I let anxious parents know that if their child is still crying a half-hour after the parent has left, I will call them. In my entire career, I've never had to call a parent for this reason.
And when you do find a care provider, ask them specifically for help in this. PM me if you are looking for articles on smoother separations and drop-off transitions.
Oh, and the book "The Kissing Hand" is a great one to start reading now. Make it part of all your goodbyes with your daughter-- even when you're just going out for groceries. She'll remember that when she gets a kiss on her hand, you WILL come back for her. Like the Hap Palmer song says "You Mommy Comes Back... she always comes back, she never would forget you!" She will learn this too, through her own experiences.
H.