For the most part, at any age, telling a child to "not fuss" or "stop crying" is both ineffective and (in my opinion) inappropriate. Children cry, fuss, throw a tantrum, or do any number of other things that we associate together as "crying" for a number of different reasons, but it's important to understand that they are always coming from the child's emotions, and those emotions are valid emotions even if they're not actions we want to encourage, and even if they are from a tantrum for reasons like "wanting a cookie" or "not wanting to go to bed".
Children have two major problems that lead to crying: they have very little control over their environment, their actions, indeed their life; and they have a limited emotional vocabulary to describe the problems they are having.
The lack of control is something that is unavoidable - after all, a one year old can't be expected to make good choices related to, well, much of anything, and even an older child won't have the capacity to understand long-term consequences of their actions - and thus we must limit their freedoms. Some parents do that in a minimalist way (such as myself), allowing their children as broad of freedom as possible while enforcing basic limits, but even then we still must require them to go to school, go to bed on time, have limited screentime, and not eat dessert for dinner. Many parents prefer to proscribe their children's choices even further.
These limits are frustrating for children, and oftentimes, tantrums are their way of exerting control over those limits. When that occurs, it is not appropriate to tell the child their frustration doesn't matter - or not to be frustrated; instead, we should follow a fairly simple script.
- Give the child space to process and calm down. Let them know that the limit you are enforcing is still there, but you're going to pause things until they are able to calmly discuss it. Don't tell them to calm down - nobody likes that! - just let them know that when they are calm, you can discuss things.
- Tell them why the limit is there, and why it's important. Give them that long term context that they don't have. Reinforce that it's not to hurt or punish them, it's because it's necessary for their long-term or short-term development or safety or - whatever.
- Make sure they know that their needs - whether it's to eat a piece of candy, to run around outside, to play a game, or to read a book - are important, and that they will be able to do that - just not right now. Kids often fail to understand that now is not forever.
Children cry because they want to be heard - and they don't know how else to be. Telling them that you do hear them, and not just telling them that but showing them, is the most important reaction you can have to a child's outburst. Oftentimes letting them have their say will be enough!
Now, of course, you've got a minimally verbal one year old, so this is only somewhat helpful - right now. But that's not to say you can't practice this, and she will be helped by it; if nothing else, the calming sound of you voice will help. You can also give her some vocabulary here - tell her how you think she's feeling, why she's upset, so that she can learn how to describe it when she's older.
You also say "a need to get going" - this is the bane of parenting, and something I struggle with mightily, with much older children. The best lesson you can learn as a parent is that being a few minutes late is not the end of the world, and often your stress to get somewhere on time will make things like this 1000% worse. Try to build in some time any time you do have a schedule, but if you don't - let the child have the time they need. That's not to say that you shouldn't remind them of the schedule and that you need to leave, but when it's causing them directly stress - take your foot off the gas and let them breathe. You'll get there sooner if you do.