How long does it take to have a period after implanon removal?

Your doctor was right in stating that you should start ovulating fairly quickly. This is what I found in the professional monograph

Return to Ovulation

In clinical trials with Implanon, the etonogestrel levels in blood decreased below sensitivity of the assay by one week after removal of the implant. In addition, pregnancies were observed to occur as early as 7 to 14 days after removal. Therefore, a woman should re-start contraception immediately after removal of the implant if continued contraceptive protection is desired.

If it takes a week or two to ovulate, it may be 4 to 6 weeks before your first missed period.
If you're looking for physical symptoms of pregnancy, look for tender/sore breasts, this is usually the first thing a woman notices different before finding out she is pregnant. Good luck to you!