I agree that you could use more staff, and in truth it all depends on how you are handling things, if the DON sees you sitting for coffee/cigarette breaks all the time then you can complain all you want and you will not get any help.
In your position, if you want to keep this job, I would do my best and one day I would keep a diary of everything I do every 10 to 15 minutes and then present it to the DON in a respectful manner and explain that you are too busy to provide safe and high quality care to the patients, you will need more help if they want to maintain the high standards that the facility is proud of.
If they turn you down
, keep up the good work
and hopefully it will be rewarded.
BTW it takes a bit more than a month to get into a groove that will make things easier at work, have patience and give it your all. As a new LPN you still have skills and more to learn. I'm sure it will get easier- GOOD LUCK!!