When should I move onto double jumps from tabletops?
Such fear is completely normal. Eventually you'll get over it, and even though it's different for different people there are some things you can try to help you cope with that first time. Here are some approaches I've either used myself or seen with others - in the end it mostly only comes down to what CardMechanic already answered: in case you can properly jump tabletops, literally the only thing holding you back from jumping similar doubles is a mental block.


First of all, and this applies to all other steps below actually, clear it properly in your head. Imagine yourself confidently and cleanly jumping the double, in the same way you do it for the tabletop. Imagine looking down and flying over the hole in the middle. Visualize it.
Measure the tabletop, e.g. put your bike next to it and see how the length compares to your bike's length. Then go find a double with roughly the same size or smaller, put your bike next to it in the same way, and make your brain realize it's being irrational.
Get good at estimating speed needed for jumping a tabletop, find a similar double (both distance and shape of the kicker, both are important in defining what a jump feels like), and just go for it at the same speed. There's no way you won't clear it.
Have someone else jump the double and ride next to him/her to figure out the correct speed. Seeing others do it at exactly your speed will make you more confident.
Make yourself irritated, to the point you are getting a bit angry even, by riding onto the double like you are going to jump it but in the last second ride around it. Eventually alternate with jumping thea tabletop as well to tell yourself 'yeah, I can do this'. Doesn't work for everyone, but chances are after a while you start to feel a bit supid and annoyed and angry and at one point, make the click and decide to go for it.
Find an appropriate double and cover the hole with for instance a pallet. Now it's basically a tabletop. Jump it a couple of times and you'll find yourself removing the pallet in no time.
Final words: know that once you clear the double for the first time, you'll be welcomed with rushes of adrenaline, dopamine and whatnot and you'll be walking on sunshine - best feeling ever, you know you want it.


edit as requested, some info from the comments: the reason why I'm mentioning finding a double similar in shape/size/length to a tabletop you know how to jump, is that you can clear both with the same body movements and hence don't have more risk of over- or undershooting it.

Overshooting a double or tabletop is the same: if you have some amount of experience and spot your mistake early enough when in the air you'll by all means want to avoid landing front wheel first since that might end up going over the bars. Instead actively force the rear wheel down - but also not too much. Even when completely overshooting and having to land on flat that has a good chance of not resulting in a crash. And it's easier than, while in the air and possible panicking a bit, trying to aim for a landing with both wheels at the same time. Actually you can train for this to some extent: take a jump you know well, then try to land a few inches further. Then some more, and so on, and take mental notes of how it feels and what happens and how you can counter it.

For undershooting it depends on how much you undershoot. If it's only a bit, e.g. hitting the top of the landing with the rear wheel (not ideal, but unless you're really short you'll just ride away) or the front wheel (dangerous, often results in an uncontrolled 'bounce') there's no difference. If you undershoot way too much though, a tabletop will save you but on a double you'd land straight into the gap. Which can end up pretty bad. But can be avoid by not trying to advance too fast, i.e. if you can jump X easily, don't attempt a double which is X * 2. Take small incremental steps, as for any practice out there.