For DNA extraction, you would need only a few eggs. PCR would then give you all the copies of your target gene(s). A quick Google Scholar search on _Takifugu_ fecundity revealed a paper by Yang and Chen (2008). They found that _T. obscurus_ produced an average of 320.8 oocytes mg$^{-1}$ ovary wet weight. In comparison, _T. ocellatus_ produced 125.2 oocytes mg$^{-1}$ ovary wet weight. _Takifugu rupripes_ and other species are likely in a similar range, which is plenty of tissue for DNA. Kusakabe (1962) published on the fecundity of _T. rubripes_ but the paper is in Japanese and is not readily available to me.
**Beware:** _T. rubripes_ ovaries are highly toxic. Why not use other tissue instead?