Since I was (very) disappointed that Whatsapp couldn't be used on my Tab (10.1 WiFi), I couldn't stop thinking about how to get this thing working after all. This morning I had a brainwave, but didn't think too much about it, since I guessed I couldn't be the first one thinking about this?! But after searching the forum this afternoon, I actually couldn't find any post mentioning what I just did. But I must admit, my search-qualities may lack (as does my English)... So sorry if this is already well known / spoken of.
I couldn't get Whatsapp installed on my SGT the normal way(s), so what I now did was Titanium Backup Whatsapp on my Phone (where I was already using it), copy that Titanium Backup files into the Titanium Backup folder on my SGT and then restored that App+Data for Whatsapp on my SGT.
Now it did install on my SGT and when I sent a message to someone, it arrives immediately!
Only thing is the message history on my Tab+Phone isn't synced (of course) and if someone sends me a message it only arrives on my Tab. It arrives on my phone again as soon as I power down my Tab (or when I would kill the Whatsapp app that's running in the background on my Tab I guess).
Again, I'm sorry if someone mentioned this before. I hope this information can be of use for some of us!