Get Your Cat Care Questions Answered By Cat Vets ASAP
Doxycycline can be used in cats and is often used to treat FIA and chlamydia. You would need to check with a pharmacist or your vet as to dosage. Dosage is based on weight, not age. Note that reconstituted (liquid) Dox is only good for about 2 weeks after mixing, so if this is something left over from an earlier treatment, it will not be effective if it's been mixed for over 3 weeks.
Hopefully this answers your question. For detailed specifications, a vet or pharmacist must make that decision. Also, this is probably not the drug of choice for a bite wound. There are others that would be more appropriate and effective.