Yes those birds are opposite gendered whence is obviously good.
Not to be overly blunt, but wanting them to experience parenthood is a terrible reason to breed.
What do you mean by "you have everything you need to keep her healthy"?
And do you have everything to keep the babies healthy?
Such as... Thousands of dollars in the bank in case something goes wrong? A professional brooder in case you have to pull them for hand feeding? The time and energy and willingness to feed a baby bird EVERY HOUR if something goes wrong early on? A digital thermometer? A high quality hand feeding formula? A crop tube of the correct size? A gram scale with decimals? Egg food or an egg food recipe? Have you already taught your budgies to eat both fresh food and pellets? Do you have the knowledge of how to spot dehydration? Sour crop? Bacterial infection? Yeast infection? Mites? This doesn't even scratch the surface of what you need before you can consider yourself responsible.
You said the female is older; how old? How big is the cage?
Just the fact that you put the box INSIDE the cage shows you are vastly underprepared for this. How are you going to check the babies to intervene if there is a problem? How are you going to clean the nest box with minimal disturbance to the parents? Or are you just going to let the babies chill in their own filth the whole time? Or are you going to majorly disturb the parents and risk them killing their babies because of it?
What is your plan to make sure you are not adding to the unwanted budgies, these "beginner birds" who usually turn into "throw away birds"? How will you come to terms with the fact you are producing more budgies when you know (if you have even bothered to find out) that they are usually unwanted by the time they are 2 years old?
This is only a small sampling. SMALL. Of the reasons why this is a bad idea. And I'm not against breeding. I am a breeder myself. I'm just saying you are clearly not taking the steps needed to be responsible about it. If you go ahead as you are, you are joining the ranks of unethical, irresponsible, selfish breeders that we commonly label "back yard breeders" who are basically only small scale versions of "bird mills" because they do not prioritize the bird but instead focus on their own desires.
I'm not trying to be harsh, but you received polite advice and seemed to ignore it, so I am forced to be a little bit less polite. I wish someone had said these things to me when k started out. Did you even read the link Ravensgryf posted for you?