Queen bee missing

[Butteredloins]

Hi guys
So one of my hives was made with a package bee set with queen. They were doing great and drew out heaps of frames so I added a super box. After doing a inspection I noticed I could find the queen and that the bees had made a queen cell. Now since they are a package bee I doubt they swarmed and there seems to be heaps more bees and not less. Looking in the hive today I see there are eggs in the super frames but none in the bottom brood box where they should be. Also they are storing heaps of honey and pollen. There are still large and capped cell which are all workers. No I guess I will have to see if these eggs turn into drones but if they don't there must be a queen which I doubt there is. The queen cell in there has hatched about 4-5 days ago and no new queen and I've checked twice. Should I order another queen? I just worry that they will soon run out of eggs

[SiWolKe]

If the QC has hatched 4-5 days ago the new queen might be absent on her mating flight.

It needs some time after hatching for her to dry out and be mated, the queen usually orientates first and the makes a few mating flights.

In bad weather this can be prolonged. I would wait 2 more weeks and now not disturb the colony. The new queen hides and is very lively, so chances to crush her are high.
While checking she might fly away or fall into the gras to be stepped upon.

The eggs in the supers might be the new eggs from her because first egg laying is often chaotic and done in an area with honey around. Only if you have no excluder, otherwise it may be some egg laying workers. But if the queen escaped while you checked and came back it may be she is in the super now.

Bees without nursing to be done can last 3 months or more so you have time to introduce a new queen.

But if you wait too long they might not accept a new queen, having laying workers.

If you have a second hive you can make the queen test. Give some comb with worker eggs and see if they build QCs again. Then you know they are queenless.

[BeeMaster2]

What SiWolke said plus, new queens often are smaller than mated queens. They are very hard to spot in a hive. If you have eggs, you probably still have the original queen and her daughter, that is a very good thing and quite normal for a supersedure. 
Jim

[Butteredloins]

Thanks guys, I just didn't want the colony to lose momentum. I do have an second hive. Also I have no excluder on. Should I just wait then and inspect in another week or should I put more brood in there?. I just don't want the colony to die and it takes awhile here to order another queen.

[BeeMaster2]

Since you know she hatched and when, you need to wait at least 20 days for her to get mated, lay eggs and have a good amount of wet brood before you inspect again. Like people, bees will blame the new queen for too many disturbances to the hive and kill her and start the process over.
Jim

[SiWolKe]

There are some things about installing a package I learned this year. Never had a package before.

First: the bees are often another race than the queen and therefore the queen is not always accepted or is superceded quickly.
Restrict the colony to one brood box, or what you have as brood area, take off all honey supers. The pheromones of the new queen in cage must fill the box. Feed syrup while introducing her, so the bees are gentle with her, release her from the cage and start building comb. No matter if there is a flow, feed,  you don?t know how many forager you have gotten with the swarm, and foragers don?t nurse or draw, which is more important at the beginning with a mated queen. The bees will prefer building up then to be an established hive and they need much food to do this, be it nectar or syrup or both.
After lodging the bees and hanging the cage, wait three days then look if she is released. Then do not disturb for 2 weeks and after that look if she lays or if there is a queen cell.
If there is a queen cell, closed or open, be quick to close the hive.
Like sawdstmakr said, wait 20 days, or better 24 days then until there might be new brood.

After the bees filled the broodbox with brood and some stores you can expand the hive. Such a colony will not swarm ( hpefully) and will not bring much honey.