I am relatively new to DnD, and the one or two games i've played before have ended at around level 4-5.
I am about to start up a campaign, and I am rolling a Gnome Fighter that is going to focus on mounted combat. I plan on picking up a riding dog. 
Now, I am worried about my dear dog Mako surviving long term and remaining useful and relevant throughout the game. 
I've been looking into methods, and it seems like Wild Cohort is a pretty good feat to take, but i'm not sure if it will scale well long term since I don't really have any experience. It seems like barding will be key, particularly some enchanted barding as soon as possible. 
Beyond that, i'm not really sure what would be best to maintain a decent mount.
I've thought about taking a level of druid for animal companion, since the companions level scales with your highest level class, but my DM maintains XP penalties for multiclassing, so that doesn't seem like it would work unfortunately. 

Any general tips, advice, or anything I can get to make my experience as grand as possible?

Just a note, my DM is wanting to limit us to the players handbooks, but anything from another book, I can show him and he will decide if I can use it or not. Basically he just doesn't want anything really extravagant, outlandish, or anything like that, to put it vaguely.