I'm pretty sure Doerr's 98. Multiple sources list his year of birth as 1918.
Incredible that he's still around. There are two ex-MLB players who are older, but they were part-time/cup of coffee guys (the oldest is 99, would turn 100 in October if he makes it). Doerr is the only player alive who played in the 1930s (debuted in 1937 when he was 19).
Anyone ever read The Teammates by David Halberstam? It's about Ted Williams, in his final days, reuniting with his 1940s Red Sox teammates Doerr, Dom Dimaggio and Johnny Pesky in 2002. It's worth reading.