How many eukaryotes are there on Earth?
Could not fit in a comment....

To make sure we all understand your question...

Is your question how many (eukaryote) species are currently living? or How many (eukaryote) cells are currently living??

Just a hint to answer the question

Micheal Lynch, in his book (On the Origin of Genome Architecture) at page 3, Box 1.1 tries to answer the question How much DNA is there on earth?. He ends up with an estimation of a total length of DNA on earth of $10^{24}$ km for procaryotes, $10^{25}$ km for eukaryote (of which $\frac{1}{1000}$% is accounted to humans). This sums up to a total DNA length of $10^{12}$ light-years, or 10 times the diameter of the known universe!

In his calculations, he estimates that the total number of procaryote cells at $10^{30}$ (citing Whitman et al. 1998 as you did). He estimates the total number of eukaryote species to $10^7$, i.e. 6 times the number of known eukaryote species. However, he doesn't directly give any reference for this estimate but he refers to different chapters in the book that contain lots of references.

...I hope that helps...