Welcome to the wonderful world of breeding. I'm glad that you're wanting to do some research first and learn what to look for - because the very WORST reason for wanting to breed is to just "get some cute baby rabbits or "have the experience of having baby rabbits". Too many people make uneducated choices based on those motivations.
The first thing you need to do is to get the "standard of perfection" from ARBA (
www.arba.net). I'm pretty sure even the prior edition would work for you since I don't think that mini lops have changed at all in their showing standards.
Learn this standard to the point that you understand how many points go towards each thing - and what the "ideal" mini-lop would look like.
Make sure your doe is the right age to breed - you don't want a first-time mama being over the age of 1 if I remember right (I'm not sure about the mini-lop breed).
Join the mini-lop club to learn more information and get in contact with experienced breeders who have worked to build their reputation. Here is a link to that site:
http://minilop.org/
Find a breeder you trust and have them go over their rabbits with you and take your rabbit (if they will let you) and ask them what they see as the strengths and weaknesses of your rabbit and have them help you find a good doe/buck that will work well with that rabbit.
Something I was explaining to a friend today is this....and I hope I make some sense.
There is a major difference between buying a rabbit to show - and buying a rabbit to breed.
You may read that an go "huh?". Isn't showing important?
Yes - it is. But when you are breeding - you are breeding two rabbits to try and create a "better" rabbit. You can have a grand champion that has the same faults as another grand champion...and produce poor bunnies. Or you can breed a grand champion to a lesser quality rabbit - and get junk bunnies (as far as showing goes).
This is why if you're choosing your rabbits to breed - you need to look beyond "championship lines" and look at "compatibility with what I have".
Some more things to consider...
I recommend having an "emergency fund" of at least $250 before breeding. I just did the "responsible" thing a couple of months ago. I bred TWO does at one time...so that if we had issues - one doe could foster the others.
When the first doe had 11 babies - I knew my idea might be out the window if the second doe had a large litter. Imagine my shock when the doe had six - BUT - her milk never came in and she wound up with an infection due to some complications (retained placenta).
I wound up spending over $230 for treating the doe...plus I now had one doe trying to raise 17 babies with my help in supplementing. (Did I mention I didn't have formula and had to go spend a bunch of money to buy what I wanted to use for the recipe I use??).
In addition - have plans ready for if your doe delivers but dies - or delivers but doesn't have milk come in - or any other scenario which may involve you having to hand feed the kits.
I'm not trying to scare you off from breeding - but so many people think, "Oh...this will be so much fun..." and maybe it is for the first few litters - till they come across a problem with a litter or lose a doe.
Finally - I'm not sure if your rabbit has done well at ARBA shows or 4-H shows. I was under the impression that ARBA standards were more "strict" (I could be wrong) - so I'd recommend showing your rabbit at an ARBA show a couple of times to see what judges have to say.
Good luck with your breeding!
