Let's start with step 1 here.:
The mechanics of 4e don't care how old you are. That's purely a role play decision, the length of your career is up to you, your DM and whatever narrative flavor you give your campaign. So this is not a hurdle if you don't want it to be.
Second, if you start to think about how long a campaign really is, it's probably a few short years of game time to go from L1-L30.
So if you want to, you don't have to do anything.
If you do want to do something, there are some interesting options:
When you would end your career, end your life and become a revenant. You might change classes, but Revenant, past life Dwarf is a solid option. Bonus roleplay points if you commit suicide to come back as undead.
MC Druid and take the ED Master Hierophant, at L24 you will stop aging, get there before you are too decrepit to continue adventuring
Depending on the source and affects of the aging you've undergone, the Remove Affliction ritual may take care of it.
There is only one source of premature aging I'm aware of from a WOTC official source. That is perilous archways from the Tomb of Horrors super adventure. This aging specifically can be cured with Remove Affliction or ages away after a set number of milestones (though repeated exposure can still kill you). However, if this is not the source of your character's aging (and you're a bit low level for this spot in the superadventure), ask your DM about what he expects the effects of this aging to be on the narrative and the mechanical effects(if any).
Since this seems more like a homebrew effect, the absolute best thing you can do is discuss remediation with your DM. She created the effect (or at least sourced it), so she will be the best possible person to discuss this with. We're not much help on the effects when there aren't well defined rules (4e is sort of light on this stuff, it's primarily driven by combat mechanics, with a secondary drive of skill mechanics, narrative mechanics are intentionally not well supported to allow for more narrative freedom).
Again, there aren't many sources on what to do about aging adventurers because 4e adventurers are assumed to be in their prime and fully capable, you'll have to work out the effects with your DM.