A dipole is twice as long as the equivalent monopole. However if the size of a dipole isn't a problem, then certainly it's possible to use one.
As Michael Kjörling mentions, you want (by convention) a vertically polarized antenna on VHF, not horizontal as the "T" you have drawn would be. But that's no problem -- we can make a vertical dipole also. The tricky bit is just getting the feedline into the middle in such a way that the feedline doesn't mess up the antenna.
There's a trivial solution: run the feedline inside the antenna. Such a thing can easily be constructed from a piece of coax:
The design is quite simple: cut a piece of coax to the length of a dipole. Then, strip the shield off half of it. If you want to be fussy, you might cut the coax-side of the dipole a bit short, since the HT body effectively makes it a bit longer. If you don't do this, you are effectively feeding the dipole a little off center, so the feedpoint impedance will be a bit higher. Not a big deal.
This design exploits a thing usually undesired in coax-fed dipoles: common-mode currents on the "feedline". You don't need a balun with this design, because the common-mode currents on the feedline are very intentionally half the dipole. Normally we don't want the feedline to be part of the antenna. Here, it is the antenna.
Alternately, you could argue this design is a case of an infinite balun.
To support the coax, you might attach it to a fiberglass rod with some heat-shrink tubing, or use semi-rigid coax that doesn't need additional support.
Thanks to a comment by user2338215, I have a great example of commercial antennas built this way. They are 2.4 GHz antennas, where even a full-length dipole is really small.
This antenna is so small that the feedline even extends up into the body. You can see here that the shield has been removed from the final quarter-wavelength of the line (that's one half of the dipole), and the other half of the dipole is made by a sleeve folded back over the feedline. You can construct the same thing by folding the coax shield back over itself, although the cable jacket makes for a relatively lossy dielectric.
This is a kind of sleeve or bazooka balun. The sleeve plus the coax shield make a coaxial transmission line. Usually they are shorted on the end at the left, which has the effect of making the sleeve not radiate. But they can be shorted on the other end (as in this picture), and then the sleeve does radiate, which is exactly what's desired in this case.