Transrectal diagnosis can be performed using a scanner with a 7.5 MHz transducer. The 7.5 MHz has a penetration of 5-7cm, meanwhile the 5 MHz has 10-17 cm deepness and the 3.5 MHz 17-20 cm.

I would recommend a transvaginal ultrasound probe for early pregnancy follow up. 

However, you would eventually need a transabdominal curved probe in later pregnancy, probably after 14 weeks or so. 2.5-5 Mhz range is usually acceptable. A variable frequency probe is preferred but may be expensive..

You will have to shave the pubic area for good probe contact, goat hair would interfere with examination.  if this is not practical, you might try using plenty of jel enough to soak all hair. 

Depending on your research, you may need an ultrasound with color doppler and maybe even with a volume probe to do 3D / 4D examinations. make sure that the machine is out of the reach of the goats legs, and remember that sudden traction or impact on the probes and cords may cause expensive damage. A sudden kick may cost you thousands of dollars. 

good luck. 

i will prefer 5 Mhz

thank you all for your valuable answers to my question