can you breed with your starter pet

So long as your starter is an adult and has not been made infertile, yes.

Yes you can breed your starter! They have to be an adult though (when you register they are an adolescent) they will age slowly untill they become an adult and then you can breed them.

There are some breeding restrictions in this game.
1) only adults can breed
2) only pets of the same species can breed
3) pets must be of opposite genders
4) pets can refuse to breed if they are too closely related. Ex:parents and children, full siblings, half siblings
5) females have breeding cooldowns, they can only breed once and then have to wait to be bred again.
6) infertile pets can not be bred (they will have a heart that is crossed out)

Below are pets of mine that are examples of the rules above.

1) Andromeda is an Adult so she can breed. The exploding messenger is only an Adolescent so he is not old enough to breed yet.
2) Andomeda is a Zolnixi so she can breed with other Zolnixis but not any other species
3) Andomeda is Female therefore she can breed with Reys a Male zolnixi but not Zarah who is also a female.
4) Andromeda has a son Un-named if you try to breed them they will refuse.
5) NightStar has recently been bred, you can see she has a cool down at the bottom of her page. The next time I can breed her will be 1/16/2020 at 10:02PM. (You can also see who she was bred with.
6) some pets are sold infertile by their breeders. You can visit Kopei and see she has a heart that is crossed out. This means that she is infertile and can never breed.

thanks