Hi Catherine,
Which State or Territory are you in?
The laws surrounding limitations differ from each State and Territory. Most limitation periods state 12 years. In any event, 8 months would most certainly be within the limitation period. However, this limitation period is only relevant if the other party decides to initiate court proceedings for damages.
If the accident was your fault and you are uninsured, the other party has a right to claim damages (including costs related to repairing their vehicle) from you. If you do not pay this, the other party may apply to the court for judgement and you may receive a summons or writ claiming damages.
To avoid an action for damages, try negotiating with the other party first and explain to them your financial situation. Perhaps you could reach a settlement for an amount lower than what they were originally claiming. If you do, it is worth having this agreement in writing, clearly spelled out and signed by both parties.