Had hysterectomy.. Kept ovaries.. Will I begin menopsuse sooner?

Possible. The average age for menopause is 50 to 52 years old. However, the average age for menopause after a hysterectomy is 48 to 50 years old.
No. The ovarian production of female hormones will dictate the onset of menopause. Since you won't have periods your doc will have to check your hormone levels to document that you are postmenopausal.