As I have already mentioned heavy coats are a big consideration when deciding to buy a Pekingese. Your new family member will, we presume, be living in the house. With central heating, or whatever, a dog living in the house will rarely carry a wealth of coat. We would recommend a little gentle grooming on a daily basis. Initially five minutes a day will suffice but as your pet gets older this time will extend.
Bathing is also fine but in moderation and at the right time.
If you feel that your Pekingese is feeling off colour, consult your Vet. Many illnesses show similar symptoms, so do not trust, entirely, your own diagnosis. Most of these can be warded off through regular worming and grooming. Vaccinations are extremely important, these keep diseases such as distemper, hepatitis, leptospirosis and parvo virus at bay.