Why is it considered bad practice to use the 'new' keyword in Arduino?
Most Arduinos (like the Uno or Nano) have very few RAM, thus you first need to make sure, that you never allocate too much memory. Also dynamically allocating memory can lead to heap fragmentation (heap being the part of memory, where dynamic allocation happens).
In most cases you would want to allocate memory of different sizes (for example arrays of different sizes) or just different objects (with each having it's own size) (!!! This is the key point here). Then you are going to delete some of these objects. That will create holes inside the memory. They can be filled again with objects with the same or less size. As time passes and more allocation and deleting happens, these holes tend to get smaller, up to the point, where none of your new to allocate objects can fit in there. That memory then is unusable. This phenomenon is called heap fragmentation.
These holes appear naturally, also on a PC. But there are 2 key differences:
The Arduino has such little RAM, that the holes can fill up your memory very very fast.
While the PC has an operating system, which manages the RAM (defragmenting it or putting unused stuff away into a paging/swap file), the Arduino does not have an OS. So noone keeps an eye on the real available RAM and noone tidies up the memory once in a while.
That does not mean, that you cannot use dynamic allocation on an Arduino, but that is very risky depending on what exactly you are doing and how long the program should work without failing.
Considering this big caveat, you are very limited on how to use dynamic allocation. Doing it too much will result in very unstable code. The remaining possibilities, where it might be safe to use it, can also easily done with static allocation. For example take your queue, which is basically a linked list. Where is the problem with allocating an array of QueueItems at the start. Each item gets a way to determine, if it is valid. When creating a new item, you just pick the first element in the array, which has a non-valid item, and set it to the desired value. You still can use the data via the pointers, just as before. But now you have it with static allocation.
You might find, that the code looks uglier that way, but you need to adapt to the platform, that you use.
Note, that this does not apply, when you are going to create only objects with the same size. Then any deleted object will leave a hole, where any new object can fit into. The compiler uses that fact. So in that case you are safe. Just every object, that you dynamically create in your program, needs to be the exact same size. That of course also includes objects, that are created inside different libraries or classes. (For this reason it can still be a bad design choice, as you or others (if you want to publish your code), may want to pair your library with other code)
Another way to be safe is to only create and delete objects in closed cycles, meaning, that a created object needs to be deleted, before the next object is created. Though that is not fitting for your application.
On bigger microcontrollers, for example the non-Arduino boards with the ESP32, have much more memory. Thus the use of dynamic allocation is not that bad on them. Though you still don't have an OS to manage the RAM.
Dynamic allocation is generally discouraged in embedded applications because you cannot guarantee that you do not exceed (attempt to allocate more than) the available memory. Static allocation will generally have this guarantee although out-of-memory bugs may still be possible.
Additionally, far fewer services or tools are available to automatically manage and mind the memory for you. Any service that does so will consume computational resources.
This means that you inherently create a mechanism in your device that would cause a memory (heap) overflow and possible undefined behavior (UB). This is true even if your code is bug-free and has no memory leaks.
In non-critical, exploration, learning, and prototype applications this may not be important.
Consider that without careful consideration undefined behavior can result in hardware failures and unsafe performance, for example if the device reconfigures GPIO through an errant write to the correct registers during a crash.
For starters, fix your library
As noted by @crasic, dynamic memory allocation is generally not recommended for embedded systems. It may be acceptable for embedded devices which have a larger amount of free memory - embedded Linux is commonly used, for example, and all Linux apps/services will tend to use dynamic memory allocation - but on small devices such as an Arduino there simply is no guarantee that this will work.
Your library illustrates one common reason why this is a problem. Your enqueue() function creates a new QueueItem() but does not check that the allocation succeeded. The result of failed allocation may either be a C++ bad_alloc exception, or it may be returning a null pointer, which when you reference it will give a system memory access exception (SIGSEGV signal in Linux, for example). It is nearly universal in Linux and Windows programming to ignore memory allocation failure (as encouraged by most textbooks), because the massive amount of free RAM and the existence of virtual memory makes this very unlikely, but this is unacceptable in embedded programming.
More generally though, as @crasic says, memory fragmentation can leave even non-buggy code unable to allocate memory. The result will be a failure to allocate memory, but the code will at least know this has happened and will probably be able to continue.
But better, use a fixed-size FIFO queue instead
Your code relies on dynamic allocation to add and remove elements in a queue. It is perfectly possible (and equally easy coding-wise) to create a fixed-size array for the queue, so the various failure modes of dynamic allocation simply do not apply. An item to be queued is simply copied into the next free queue slot, and a queue slot is marked free when it has been used. (Don't forget to use a mutex when adding and removing items from the queue, because adding and removing will often be called from different places.)
The queue can be made whatever size you feel is appropriate (allowing for how much RAM you have). With a fixed size, you are forced to make a design decision on what should happen if the queue overflows - do you delete the oldest data to make room for the new value, or do you ignore the new value? This may seem an unwelcome new feature, but it is a good thing, because the third option which you've currently got is that your code goes "Aaaarrggghhh I don't know what to do!" and crashes fatally, and we don't really want that.