I'm so excited my eggs just shipped.

What is the best way to get them under her and take out the dummy eggs she is on? Should I do it at night or wait until she comes out to eat? If she is used to being moved would it be ok to just pick her up, take out the dummy eggs and put in the good ones? Also would it bother her if I check in on her while she is nesting or would she be bothered enough to abandon the eggs or chicks?
It all depends on the hen, and what she's used to. Theoretically, you should either do it when she's off the nest, or you should do it at night. But a hen that is tame and picked up off the nest every day probably won't think anything of you reaching under her anytime.
There are a few things that I would recommend, regardless of her temperament. First, evaluate the eggs carefully. (Always wash your hands thoroughly before handling hatching eggs, and be sure that your hands are entirely dry before touching the egg. Any moisture on your hands can compromise the bloom, which is the shell sealant that keeps the egg from getting infected from surface bacteria. Do not wash hatching eggs. If they're so dirty that they need washing, don't use them. Mildly dirty eggs are fine if the bloom isn't compromised.) Since these are shipped eggs, some may not arrive in good enough condition to use, and should not take up nest space. Read about shipped eggs here:
https://www.backyardchickens.com/a/hatching-eggs-101. Be sure to candle them to evaluate the air cell, and let them sit quietly for a day at 50-60 degrees before starting the incubation. If she is a first time broody, do not give her more than 6-8 eggs (or possibly less if the eggs are large and she is small). Assign each egg a number or letter. Draw a line around the equator of each egg that is used, and write that egg's number or letter repeatedly along that line. You may never need to identify any specific egg, but there are many unexpected circumstances where you do, and it's nice to have it set up ahead of time, where it can be seen when the egg is in any position.
Be sure that the nest has adequate padding for real eggs, and that the padding doesn't slip out of place as the hen shifts around on the eggs. If eggs get too close to the floor of the nest they can be cracked under the broody's weight. There are many, many different options. I have started using 2 inches of aspen shavings, topped by 2 inches of very high quality timothy hay (American Pet brand is soft, non-stemmy, clumps around any messes, and smells fantastic), which can be found in the rabbit food department of large pet stores like
Petco. If you need to make any nest modifications, do it before you put in the new eggs, just to be sure that she accepts the upgraded nest.
If you take her off the nest to switch out the eggs, do not do it in front of her. Some broodies, even tame ones, will become frantic if they see their eggs being moved around. If they're standing up and they try to intervene, they could end up breaking eggs.
Before I put stored eggs, which are 50-60 degrees, in an incubator or under a hen, I like to slowly warm them up a bit. I can do this by either moving them to increasingly warmer rooms over a few hours, or by putting them in a dresser drawer with a heating pad (not on a heating pad, but with one inside the drawer to heat up the air inside). After they reach 80-85 degrees, then I put them in the incubator or under the hen. Rapidly heating cool eggs can cause condensation on the surface, which can affect the bloom.
Have a separate container to put the dummy eggs in so you don't end up mixing them with the hatching eggs. No need to risk breakage or have anything slow you down. Take out all the dummy eggs before adding any of the hatching eggs so there is no mixup or fumbling. This is especially important if you do it by reaching under the hen while she's sitting on the nest. If you do it at night, be sure that your flashlight doesn't shine in the hen's eyes, and that it can't fall out of your hand or pocket and break eggs (voice of experience here -- just missed them by an inch!). If she's on the nest while you do this, you don't have to put a hatching egg back in the exact same place where you found a dummy egg. Just gently place the eggs, one at a time, under her wings or right in front of her chest and she will wiggle them in to their ideal position. Just don't put all the eggs in one place.
How much you can check on a broody while she's nesting before she gets annoyed depends on the broody, and your relationship with her. My broodies are very tame, and were totally fine with me hanging out with them or taking them off the nest to eat, etc. But some broodies do not tolerate interference at all, and most are somewhere between the two extremes. If she's not tame, don't bother her any more than is absolutely necessary to provide food, water, remove any broody poo from the nest (which rarely happens, but needs to be removed ASAP if it does occur), etc. Brooding is not the time to try to tame an anxious hen!! On the other hand, if she is already tame and enjoys your company, she may be fine with you checking on her, or she may be in hormonal hell and not want you around at all. If she seems upset, don't push it.