Yes, you are considered an adult.
(Sources in this answer come from "Bar Mitzvah: Maturity of Body or Mind," by R' Yehoshua Pfeffer. I recommend reading the whole essay for a nice overview of how we determine adulthood.)
"You travel" implies that there is a persistent entity called "you" that is transplanted from one time to another. If you are persistent, then presumably, you bring with you both your body and your accumulated mental capacity.
According to the Mishna in Niddah 6:11, standard signs of physical maturity, which are present in the vast majority of 31-year-olds, make one "obligated in all of the commandments stated in the Torah." Given that you possess the body of a 31-year-old, that is sufficient for this purpose.
There is also the chronological standard of thirteen years, as indicated in the Mishna in Avot 5:21, which various authorities, including the Ro"Sh (Teshuvos 16:1) consider to have its own status, derived from halacha leMoshe miSinai. I would argue that this standard is met (or at least sidestepped) in this case as well, for three reasons:
The persistent entity known as "you" has, subjectively, lived for thirteen years.
The Talmud, in Niddah 45b says that the reason that the age of majority for girls is before the one for boys is that "God put more understanding into Woman than into Man," implying that the significance of chronological age is the mental capacity gained in that time. As indicated above, I think we must assume that you bring with you the mental capacity of a 31-year-old.
Tosafot on Sandhedrin 69a, s.v. "... בידוע," say that when, in previous years, children would attain signs of physical maturity earlier, the [effective] age of majority was correspondingly earlier. This would seem to indicate that, at least according to Tosafot, the physical signs are sufficient, irrespective of the chronological age, to convey the status of adulthood.