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Everything I've read here says that surgery should wait until you're finished breastfeeding because it will be VERY hard to ensure that you're getting enough nutrients for yourself AND your baby post-op.  I hope that you have consulted many medical professionals to ask these questions - your PCP, your obgyn, your surgeon, etc.  

Ditto what Gwen said about breastfeeding.  Your baby has had a fantastic start with nursing so far, so switching to formula around the time real food is introduced would be a good transition.  I wouldnt recommend taking an infant across the border if you have resources at home.  They will be fine for a few days if they are on formula.  For holding, you are supposed to lift/push/pull no more than 8lbs for 8 weeks, so you will need some assistance.  If your child is walking around, snuggling on the sofa with you should work out fine if they can climb up themselves.  You can change them and everything right there, too, without risking injury.

My son was 11 months 3 weeks when I had my surgery and I stopped breastfeeding him 3 days before surgery.  He was on solid food and was really only taking his pre bed feed at that time.

He was able to crawl up on the sofa for a cuddle, but he was a lot bigger than your little one, so I couldn't have picked him up the first few weeks.

 I would not have taken him with me for surgery.  I left him at home with his dad and big brother.   It's stressful enough without putting an infant into the mix.

I was on lifting restriction for 6 weeks, I couldn't lift anything over 5lb for worry of ripping my stitches.

Would you have someone with you in Mexico to look after your child? You are going to be completely incapacitated for a full day, likely more, and probably unable to watch the baby.