Yep it's normal.
Unless you need advice on any current medication your GP has no reason to see you. You're pregnant, not ill. With any luck you'll get through your entire pregnancy without seeing a single Doctor.
You can self refer for the maternity hospital you want to progress your pregnancy with. Go to their website and complete the form.
It's worth having a look at different ones. Reading reviews and many have Facebook groups. Keep in mind though that in your 3rd trimester you will have multiple midwife appointments so don't choose something so far away it becomes an epic journey every time you have to go. The last month of my pregnancy I was going every 48hrs....so choose the place you want but take distance into account.
Nothing will happen until your 12 week scan, although once you've done your self referral you'll receive some info in the post about diet, healthy habits etc.
Around your 12 week scan you'll have a midwife appointment a longish one for about an hour, they'll likely take bloods, urine. From there you'll have an appointment about once every 3-4 weeks.
20 weeks you'll have a 20 week scan. Your midwife appointments may increase.
About 30 weeks you'll be going every 2 weeks.
You'll only see your GP if you need any meds prescribe - e.g you get an infection.
You'll also need to organise a whooping cough vaccine but your midwife will discuss that with you around your 12 week scan.
Nothing happens during the first 3 months, unless something is going wrong or you are feeling unwell. Best thing you can do is get some pregnancy day-by-day books.
Congratulations!