That's the cover nubmer.

I even unscrewed the cover off the panel to have a look inside and I still couldn't find any labels with reference to a model number of the actual panel itself. Any ideas?

A tandem breaker mounts on rails and has a curved metal "clip" at the end that must fit in a slot. If you don't have the slots you can't use them. The wiring diagram should spell this out or the attached link should have all the info.

Here is a link that might be useful: Square D

The label should be in the inside if the door, though if the door has been replaced it may be missing.

Residential panels used to be limited to 42 breakers (not including the mains).

Many panels have mechanical designs to limit the number of half size breakers that can be installed to remain below this limit.

Even older panels were not designed with the mechanical stops sine the half size breakers did not even exist yet.

Some AHJs have an issue with using half size breakers in these panels since they are technically not listed to use them.

I too thought it was logical to have the label inside the door. There is a label there, but it appears to be for the door part only. The only model number on it is the one I posted originally, QOC30UF. There is no other label on the inside of the door. This is one big label that has all the spaces to identify the circuits as well. I've looked everywhere I could, even taking the screws out and looking inside at the actual panel and there is no label anywhere that specifies what exact panel I have. All I know is that it has 30 spaces and has a 200 Amp main. From looking at the Square D docs, it looks like there are two models that have these specs... Unfortunately the difference between the two is that one can support 10 tandems and the other cannot, which is precisely what I am trying to determine.

Any other ideas?

The label with the circuit diagram should tell you if you can use tandem breakers... if it's new enough. Tandem breakers fit at the bottom of the newer panels. Like I said before, look at the panel and see if you have the little cutouts for the special end of the late model tandem breaker.

Another option which may or may not be legal is to buy the QO tandem breakers that fit in older panels not specifically designed for them. For some reason they are much more expensive, but may solve your problem. The spec sheet for these breakers should list which panels are allowed to use them. Home Depot or Lowe's has them.

Square D makes a 3040 panel that has 30 spaces and 40 circuits if used with tandem breakers. I guess you either have this model or the one that only supports 30 circuits.

Some AHJs have an issue with using half size breakers in these panels since they are technically not listed to use them.

Our AHJ has prohibited tandem breakers entirely, even if the panel is rated for them. Not quite sure of the logic or when it happened, I noticed looking at the amendments to the 2008 NEC. The prohibition may have been there before and I never noticed it.