The first one is closer to grammatical and would be significantly better understood than the second. A truly correct way to say this would be:
It is better to peak at this level than to not peak at this level, and then to not qualify for the quarter-finals.
If we take out the prepositional phrases, we can see better why your examples are incorrect:
It is better to peak than not peaking and then not qualifying.
It is better to peak than not peaking and do not qualify.
The last one is pretty obviously incorrect. The first one is a bit subtler. It has to do with parallelism, but if you look at the famous Hamlet quote
"To be or not to be"
it would sound funny as
"To be or not being"
Stylistically, it sounds a little odd to repeat "at this level" and it makes the sentence harder to understand. If you're trying to say that peaking at this level would be better than holding back, and not qualifying in the process, it might express your meaning a little better to say:
Peaking at this level and qualifying for the quarter-finals would be better than not peaking and not qualifying at all.