I hate relaying this kind of stuff reported in The Sun from an unnamed "source."
To quote the source in The Sun, "They (David Tennant and Georgia Moffett) are besotted with each other and can't wait to tie the knot." It doesn't exactly say they are engaged though. I would file it under rumour for now until there's some sort of official confirmation.
If it is true, we wish them all the best. Georiga Moffett had just turned 26 this past Christmas (Happy Birthday, Georgia Moffett). We interviewed her last year at Gallifrey 21 in Doctor Who: Podshock 187.
The following is from the article that ran in The Sun:
The date was 23 April 2009. The Telegraph runs the following story about Gillian Anderson being cast as The Rani in Doctor Who (see link and quote below). Since that time we have seen a year of specials starring David Tennant and a whole new series starring Matt Smith. Where's Gillian Anderson? We are still waiting...
Do you fancy bringing back the tradition of the Doctor's face appearing in the opening credits of Doctor Who?